View source for Black hole

{{Short description|Compact astronomical body}}
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{{Use British English|date=August 2024}}
{{Use dmy dates|date=October 2025}}
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| image1            = Black hole - Messier 87 crop max res.jpg
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| alt1              = Blackness of space with black marked as centre of donut of orange and red gases
| caption1          = An image of the core region of [[Messier 87]], a [[supermassive black hole]], processed from a sparse array of [[radio telescopes]] known as the [[Event Horizon Telescope|EHT]] with colors indicating [[brightness temperature]].<ref>{{cite journal |last1=The Event Horizon Telescope Collaboration |last2=Akiyama |first2=Kazunori |last3=Alberdi |first3=Antxon |last4=Alef |first4=Walter |last5=Asada |first5=Keiichi |last6=Azulay |first6=Rebecca |last7=Baczko |first7=Anne-Kathrin |last8=Ball |first8=David |last9=Baloković |first9=Mislav |last10=Barrett |first10=John |last11=Bintley |first11=Dan |last12=Blackburn |first12=Lindy |last13=Boland |first13=Wilfred |last14=Bouman |first14=Katherine L. |last15=Bower |first15=Geoffrey C. |date=10 April 2019 |title=First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole |journal=The Astrophysical Journal Letters |volume=875 |issue=1 |pages=L4 |doi=10.3847/2041-8213/ab0e85 |doi-access=free |arxiv=1906.11241 |bibcode=2019ApJ...875L...4E |issn=2041-8205}}</ref><ref>{{cite web |date=10 April 2019 |title=Astronomers capture first image of a black hole |url=https://new.nsf.gov/news/astronomers-capture-first-image-black-hole#image-caption-credit-block |access-date=28 January 2025 |website=new.nsf.gov |language=en}}</ref>

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| caption2          = Simulated view of a [[Schwarzschild black hole]] in front of the [[Large Magellanic Cloud]]. Note the gravitational lensing effect, which produces two enlarged but highly distorted views of the Cloud. Across the top, the [[Milky Way]] disk appears distorted into an arc.<ref name=riazuelo>{{cite journal |author-link= Alain Riazuelo |first= Alain |last= Riazuelo |title= Seeing relativity -- I. Ray tracing in a Schwarzschild metric to explore the maximal analytic extension of the metric and making a proper rendering of the stars |journal= International Journal of Modern Physics D |date= 2019|volume= 28 |issue= 2 |page=1950042 |doi= 10.1142/S0218271819500421 |arxiv= 1511.06025 |bibcode= 2019IJMPD..2850042R |s2cid= 54548877 }}</ref>
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A '''black hole''' is an [[astronomical body]] so compact that its gravity prevents anything from escaping, even light. [[Albert Einstein]]'s theory of [[general relativity]] predicts that a sufficiently compact [[mass]] will form a black hole.<ref name="NYT-20150608">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=Black Hole Hunters |url=https://www.nytimes.com/2015/06/09/science/black-hole-event-horizon-telescope.html |date=8 June 2015 |work=[[NASA]] |access-date=8 June 2015 |url-status=live |archive-url=https://web.archive.org/web/20150609023631/http://www.nytimes.com/2015/06/09/science/black-hole-event-horizon-telescope.html |archive-date=9 June 2015}}</ref> The [[boundary (topology)|boundary]] of no escape is called the [[event horizon]]. In general relativity, a black hole's event horizon seals an object's fate but produces no locally detectable change when crossed.<ref name ="HamiltonA">{{cite web|author=Hamilton, A.|url=http://jila.colorado.edu/~ajsh/insidebh/schw.html|title=Journey into a Schwarzschild black hole|website=jila.colorado.edu|access-date=28 June 2020|archive-date=3 September 2019|archive-url=https://web.archive.org/web/20190903235853/https://jila.colorado.edu/~ajsh/insidebh/schw.html|url-status=live}}</ref> In many ways, a black hole acts like an ideal [[black body]], as it reflects no light.<ref>{{cite book |title=Gravity from the ground up |first1=Bernard F. |last1=Schutz |author-link1=Bernard F. Schutz |publisher=[[Cambridge University Press]] |date=2003 |isbn=978-0-521-45506-0 |page=110 |url=https://books.google.com/books?id=P_T0xxhDcsIC |url-status=live |archive-url=https://web.archive.org/web/20161202222711/https://books.google.com/books?id=P_T0xxhDcsIC |archive-date=2 December 2016}}</ref><ref>{{cite journal |last=Davies |first=P. C. W. |author-link1=Paul Davies |date=1978 |title=Thermodynamics of Black Holes |url=http://cosmos.asu.edu/publications/papers/ThermodynamicTheoryofBlackHoles%2034.pdf |journal=[[Reports on Progress in Physics]] |type=Review |volume=41 |issue=8 |pages=1313–1355 |bibcode=1978RPPh...41.1313D |doi=10.1088/0034-4885/41/8/004 |s2cid=250916407 |archive-url=https://web.archive.org/web/20130510184530/http://cosmos.asu.edu/publications/papers/ThermodynamicTheoryofBlackHoles%2034.pdf |archive-date=10 May 2013}}</ref> [[Quantum field theory in curved spacetime]] predicts that event horizons emit [[Hawking radiation]], with [[thermal radiation|the same spectrum]] as a black body of a [[temperature]] inversely proportional to its mass. This temperature is of the [[Orders of magnitude (temperature)|order of billionth]]s of a [[kelvin]] for [[stellar black hole]]s, making it essentially impossible to observe directly.

Objects whose [[gravitational field]]s are too strong for light to escape were first considered in the 18th century by [[John Michell]] and [[Pierre-Simon Laplace]]. In 1916, [[Karl Schwarzschild]] found the first modern solution of general relativity that would characterise a black hole. Due to his influential research, the [[Schwarzschild metric]] is named after him. [[David Finkelstein]], in 1958, first published the interpretation of "black hole" as a region of space from which nothing can escape. Black holes were long considered a mathematical curiosity; it was not until the 1960s that theoretical work showed they were a generic prediction of general relativity. The first black hole known was [[Cygnus X-1]], identified by several researchers independently in 1971.<ref name="Webster1972">{{citation |last1=Webster |first1=B. Louise |title=Cygnus&nbsp;X-1—a Spectroscopic Binary with a Heavy Companion? |date=1972 |journal=[[Nature (journal)|Nature]] |volume=235 |issue=5332 |pages=37–38 |type=Letter |bibcode=1972Natur.235...37W |doi=10.1038/235037a0 |s2cid=4195462 |last2=Murdin |first2=Paul |author-link2=Paul Murdin}}</ref><ref name="Bolton1972">{{citation |last=Bolton |first=C. T. |title=Identification of Cygnus&nbsp;X-1 with HDE&nbsp;226868 |date=1972 |journal=[[Nature (journal)|Nature]] |volume=235 |issue=5336 |pages=271–273 |type=Letter |bibcode=1972Natur.235..271B |doi=10.1038/235271b0 |s2cid=4222070}}</ref>

Black holes typically form when [[Supernova|massive stars collapse]] at the end of their [[Stellar evolution|life cycle]]. After a black hole has formed, it can grow by absorbing mass from its surroundings. Supermassive black holes of millions of [[solar mass]]es may form by absorbing other stars and merging with other black holes, or via [[Direct collapse black hole|direct collapse]] of [[gas cloud]]s. There is consensus that [[supermassive black hole]]s exist in the centres of most [[galaxies]].

The presence of a black hole can be inferred through its interaction with other [[matter]] and with electromagnetic radiation such as visible light. Matter falling toward a black hole can form an [[accretion disk]] of infalling plasma, heated by [[friction]] and emitting light. In extreme cases, this creates a [[quasar]], some of the brightest objects in the universe. Stars passing too close to a supermassive black hole can be shredded into streamers that shine very brightly before being "swallowed".<ref name="pmid32001633">{{cite journal |author=Clery D |year=2020 |title=Black holes caught in the act of swallowing stars |journal=[[Science (journal)|Science]] |volume=367 |issue=6477 |page=495 |bibcode=2020Sci...367..495C |doi=10.1126/science.367.6477.495 |pmid=32001633 |s2cid=210984462 |doi-access=free<!-- it appears -->}}</ref> If other stars are orbiting a black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as [[neutron star]]s. In this way, astronomers have identified numerous stellar black hole candidates in [[binary star|binary systems]] and established that the radio source known as [[Sagittarius A*]], at the core of the [[Milky Way]] galaxy, contains a supermassive black hole of about 4.3{{nbsp}}million [[Solar energy|solar]] masses.

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== History ==
The idea of a body so massive that even light could not escape was briefly proposed by English astronomical pioneer and clergyman [[John Michell]] and independently by French scientist [[Pierre-Simon Laplace]]. Both scholars proposed very large stars, analogous to modern models of [[supermassive black hole]]s.<ref name="origin">{{cite journal |last1=Montgomery |first1=Colin |last2=Orchiston |first2=Wayne |last3=Whittingham |first3=Ian |year=2009 |orig-date=Available online 18 April 2023 |title=Michell, Laplace and the origin of the black hole concept |url=https://researchonline.jcu.edu.au/9892/1/Microsoft_Word_-_Paper__Black_Hole_Concept_Final_.pdf |journal=[[Journal of Astronomical History and Heritage]] |type=Research article |volume=12 |issue=2 |pages=90–96 |bibcode=2009JAHH...12...90M |doi=10.3724/SP.J.1440-2807.2009.02.01 |s2cid=55890996 |doi-access=free}}</ref>

Michell's idea, in a short part of a letter published in 1784, calculated that a star with the same density but 500 times the radius of the sun would not let any emitted light escape; the surface [[escape velocity]] would exceed the speed of light. Michell correctly noted that such supermassive but non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies.<ref name="origin" /><ref>{{cite journal |last=Michell |first=J. |author-link1=John Michell |date=1784 |title=On the Means of Discovering the Distance, Magnitude, &c. of the Fixed Stars, in Consequence of the Diminution of the Velocity of Their Light, in Case Such a Diminution Should be Found to Take Place in any of Them, and Such Other Data Should be Procured from Observations, as Would be Farther Necessary for That Purpose |journal=[[Philosophical Transactions of the Royal Society]] |volume=74 |pages=35–57 |bibcode=1784RSPT...74...35M |doi=10.1098/rstl.1784.0008|jstor=106576|doi-access=free}}</ref><ref name=thorne_123_124>{{harvnb|Thorne|1994|pp=123–124}}</ref>

In 1796, Laplace mentioned that a star could be invisible if it were sufficiently large while speculating on the origin of the Solar System in his book {{lang|fr|Exposition du Système du Monde}}. [[Franz Xaver von Zach]] asked Laplace for a mathematical analysis, which Laplace provided and published in a journal edited by von Zach.<ref name="origin"/>

Scholars of the time were initially excited by the proposal that giant but invisible 'dark stars' might be hiding in plain view, but enthusiasm dampened in the early 19th century, when light was discovered to be wavelike.<ref>{{cite book |title=Light and Electron Microscopy |first1=Elizabeth M. |last1=Slayter |first2=Henry S. |last2=Slayter |publisher=[[Cambridge University Press]] |year=1992 |isbn=978-0-521-33948-3 |url=https://books.google.com/books?id=LlePVS9oq7MC |url-status=live |archive-url=https://web.archive.org/web/20171130151044/https://books.google.com/books?id=LlePVS9oq7MC |archive-date=30 November 2017}}</ref> Since light was understood as a wave rather than a particle, it was unclear what, if any, influence gravity would have on escaping light waves.<ref name=origin /><ref name=thorne_123_124 />

=== General relativity ===
{{see also|History of general relativity}}
{{General relativity sidebar|phenomena}}

In 1911, [[Albert Einstein]] published a paper about the properties of acceleration in [[special relativity]], noting that an object accelerating through space outside of a gravitational field would be physically indistinguishable from an object in a static gravitational field. The paper also predicted the [[gravitational lensing|deflection of light]] by massive bodies.<ref name="Einstein 1911 898–908">{{Citation |last=Einstein |first=Albert |title=Einfluss der Schwerkraft auf die Ausbreitung des Lichtes (On the Influence of Gravity on the Propagation of Light) |journal=[[Annalen der Physik]] |volume=35 |issue=10 |pages=898–908 |year=1911 |url=https://zenodo.org/record/1424213 |bibcode=1911AnP...340..898E |doi=10.1002/andp.19113401005 |author-link=Albert Einstein}} (also in ''Collected Papers'' Vol. 3, document 23)</ref> In 1915, Einstein refined these ideas into his [[general theory of relativity]], which explained how matter affects spacetime, which in turn affects the motion of other matter.<ref>{{Cite journal |last=Einstein |first=Albert |author-link=Albert Einstein |date=1915 |title=Feldgleichungen der Gravitation |trans-title=Field Equations of Gravitation |journal=Preussische Akademie der Wissenschaften, Sitzungsberichte |pages=844–847}}</ref><ref>{{Cite journal |last1=Janssen |first1=Michel |last2=Renn |first2=Jürgen |author-link2=Jürgen Renn |date=2015 |title=Arch and scaffold: How Einstein found his field equations |journal=[[Physics Today]] |type=Feature article |volume=68 |issue=11 |pages=30–36 |bibcode=2015PhT....68k..30J |doi=10.1063/PT.3.2979 |hdl=11858/00-001M-0000-002A-8ED7-1 |doi-access=free |hdl-access=free}}</ref><ref>{{Cite web |last1=O'Connor |first1=J J |last2=Robertson |first2=E F |author-link2=E. F. Robertson |date=May 1996<!-- last update --> |title=General Relativity |url=https://mathshistory.st-andrews.ac.uk/HistTopics/General_relativity/ |url-status=live |archive-url=https://web.archive.org/web/20200712062639/https://mathshistory.st-andrews.ac.uk/HistTopics/General_relativity/ |archive-date=12 July 2020 |access-date=22 October 2025 |website=MacTutor |publisher=School of Mathematics and Statistics, [[University of St Andrews]], Scotland}}</ref> This theory formed the basis for black hole physics, although Einstein himself would later try, and fail, to refute the idea that black holes could exist.<ref>{{Cite book |last1=Fraknoi |first1=Andrew |author-link1=Andrew Fraknoi |url=https://assets.openstax.org/oscms-prodcms/media/documents/Astronomy2e-WEB.pdf |title=Astronomy 2e |last2=Morrison |first2=David |author-link2=David Morrison (astrophysicist) |last3=Wolff |first3=Sidney C. |author-link3=Sidney C. Wolff |date=2022 |publisher=[[OpenStax]] |isbn=978-1-951693-50-3 |edition=2e |pages=839–846 |chapter=24.5 Black Holes |oclc=1322188620 |display-authors=}}</ref><ref>{{Cite web |last=O'Neill |first=Ian |date=10 April 2019 |title=Black Holes Were Such an Extreme Concept, Even Einstein Had His Doubts |url=https://www.history.com/articles/black-holes-albert-einstein-theory-relativity-space-time |url-status=live |archive-url=https://web.archive.org/web/20250813095832/https://www.history.com/articles/black-holes-albert-einstein-theory-relativity-space-time |archive-date=13 August 2025 |access-date=22 October 2025 |website=[[History Channel|History]] |publication-date=28 May 2025 <!-- last updated -->}}</ref><ref>{{Cite journal |last=Einstein |first=Albert |author-link=Albert Einstein |date=10 May 1939 |title=On a Stationary System With Spherical Symmetry Consisting of Many Gravitating Masses |journal=[[Annals of Mathematics]] |volume=40 |issue=4 |pages=922–936 |doi=10.2307/1968902 |jstor=1968902 }}</ref>

Only a few months after Einstein published the [[Einstein field equations|field equations]] describing general relativity, [[Karl Schwarzschild]] found a [[Schwarzschild metric|solution]] describing the [[gravitational field]] of a [[point mass]] and a spherical mass.<ref name="Levy">{{cite journal |last1=Levy |first1=Adam |date=11 January 2021 |title=How black holes morphed from theory to reality |url=https://knowablemagazine.org/article/physical-world/2021/how-black-holes-morphed-theory-reality |journal=[[Knowable Magazine]] |doi=10.1146/knowable-010921-1 |url-access=subscription |access-date=25 March 2022 |doi-access=free}}</ref><!-- Levy citation should probably be revised to reflect it is a citation for a podcast and podcast transcript. --><ref name="Schwarzschild1916">{{cite journal |last=Schwarzschild |first=K. |author-link1=Karl Schwarzschild |date=1916 |title=Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie |trans-title=On the gravitational field of a mass point according to Einstein's theory<!-- via translate.google --> |url=https://archive.org/stream/sitzungsberichte1916deutsch#page/188/mode/2up |journal=Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften |volume=7 |pages=189–196 |bibcode=1916SPAW.......189S |via=Internet Archive}}
* Translation: {{cite arXiv |eprint=physics/9905030 |first1=S. |last1=Antoci |first2=A. |last2=Loinger |title=On the gravitational field of a mass point according to Einstein's theory |date=12 May 1999<!-- date submitted --> }} and {{cite journal |last=Schwarzschild |first=K. |author-link1=Karl Schwarzschild |date=1916 |title=Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie |url=https://archive.org/stream/sitzungsberichte1916deutsch#page/424/mode/2up |journal=Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften |volume=18 |pages=424–434 |bibcode=1916skpa.conf..424S}}
* Translation: {{cite arXiv |eprint=physics/9912033 |first1=S. |last1=Antoci |title=On the gravitational field of a sphere of incompressible fluid according to Einstein's theory |year=1999 }}</ref> A few months after Schwarzschild, [[Johannes Droste]], a student of [[Hendrik Lorentz]], independently gave the same solution for the point mass and wrote more extensively about its properties.<ref>{{cite journal |last=Droste |first=J. |date=1917 |title=The field of a single centre in Einstein's theory of gravitation, and the motion of a particle in that field |url=http://www.dwc.knaw.nl/DL/publications/PU00012325.pdf |url-status=live |department=Physics |journal=Proceedings of the Section of Sciences |publisher=[[Koninklijke Akademie van Wetenschappen]] |volume=19 |issue=1 |pages=197–215 |bibcode=1917KNAB...19..197D |archive-url=https://web.archive.org/web/20130518034708/http://www.dwc.knaw.nl/DL/publications/PU00012325.pdf |archive-date=18 May 2013 |access-date=16 September 2012}}</ref><ref>{{cite book |title=Studies in the history of general relativity |editor1-last=Eisenstaedt |editor1-first=Jean |editor2-last=Kox |editor2-first=A. J. |isbn=978-0-8176-3479-7 |date=1992 |publisher=Birkhäuser |chapter=General Relativity in the Netherlands: 1915–1920 |last=Kox |first=A. J. |chapter-url=https://books.google.com/books?id=vDHCF_3vIhUC&pg=PA41 |page=41 |access-date=23 February 2016 |archive-date=10 August 2016 |archive-url=https://web.archive.org/web/20160810215219/https://books.google.com/books?id=vDHCF_3vIhUC&pg=PA41 |url-status=live }}</ref> At a certain radius from the center of the mass, the Schwarzschild solution became [[singularity (mathematics)|singular]], meaning that some of the terms in the Einstein equations became infinite. The nature of this radius, which later became known as the [[Schwarzschild radius]], was not understood at the time.<ref name="HooftHist">{{cite web |last='t Hooft |first=G. |author-link1=Gerard 't Hooft |date=2009 |title=Introduction to the Theory of Black Holes |url=http://www.phys.uu.nl/~thooft/lectures/blackholes/BH_lecturenotes.pdf |url-status=live |archive-url=https://web.archive.org/web/20090521082736/http://www.phys.uu.nl/~thooft/lectures/blackholes/BH_lecturenotes.pdf |archive-date=21 May 2009 |access-date=24 June 2010 |publisher=Institute for Theoretical Physics / Spinoza Institute |pages=47–48}}</ref><ref name="paap18">{{Cite journal |last1=Petrescu |first1=Relly Victoria |last2=Aversa |first2=Raffaella |last3=Apicella |first3=Antonio |last4=Petrescu |first4=Florian Ion |date=11 June 2018 |title=Nasa Has Found the Most Distant Black Hole |journal=Journal of Aircraft and Spacecraft Technology |type=Review |volume=2 |issue=1 |pages=31–39 |doi=10.3844/jastsp.2018.31.39 |eissn=2523-1200 |ssrn=3184263 |doi-access=free}}</ref>

In 1924, [[Arthur Eddington]] showed that the singularity disappeared after a change of coordinates. In 1933, [[Georges Lemaître]] realised that this meant the singularity at the Schwarzschild radius was a non-physical [[coordinate singularity]].<ref name="paap18" /> Arthur Eddington commented on the possibility of a star with mass compressed to the Schwarzschild radius in a 1926 book, noting that Einstein's theory allows us to rule out overly large densities for visible stars like [[Betelgeuse]] because the extreme force of gravity would make light unable to escape from the star, redshift the star's entire light spectrum out of existence, and "produce so much curvature of the spacetime metric that space would close up around the star, leaving us outside (i.e., nowhere)."<ref name="eddington1926">{{cite book |first=Arthur |last=Eddington |author-link=Arthur Eddington |date=1926 |title=The Internal Constitution of the Stars |series=Science |volume=52 |issue=1341 |pages=233–40 |url=https://books.google.com/books?id=RjC9DpnWFbkC&pg=PA6 |publisher=Cambridge University Press |url-status=live |archive-url=https://web.archive.org/web/20160811034409/https://books.google.com/books?id=RjC9DpnWFbkC&lpg=PP1&pg=PA6 |archive-date=11 August 2016 |pmid=17747682 |doi=10.1126/science.52.1341.233|bibcode=1920Sci....52..233E }} {{isbn|978-0-521-33708-3}}</ref><ref>{{cite book |last1=Thorne |first1=Kip S. |author-link=Kip Thorne |url=https://archive.org/details/blackholestimewa0000thor |title=Black Holes and Time Warps: Einstein's Outrageous Legacy |last2=Hawking |first2=Stephen |author-link2=Stephen Hawking |date=1994 |publisher=[[W. W. Norton & Company]] |isbn=978-0-393-31276-8 |editor-last=Agrawal |editor-first=Milan |edition=1st |pages=[https://archive.org/details/blackholestimewa0000thor/page/134 134]–135 |quote=The first conclusion was the Newtonian version of light not escaping; the second was a semi-accurate, relativistic description; and the third was typical Eddingtonian hyperbole{{nbsp}}[...] when a star is as small as the critical circumference, the curvature is strong but not infinite, and space is definitely not wrapped around the star. Eddington may have known this, but his description made a good story, and it captured in a whimsical way the spirit of Schwarzschild's spacetime curvature." |access-date=12 April 2019 |url-access=registration}}</ref>

In 1931, using special relativity, [[Subrahmanyan Chandrasekhar]] calculated that a non-rotating body of [[electron-degenerate matter]] above a certain limiting mass (now called the [[Chandrasekhar limit]] at {{Solar mass|1.4}}) has no stable solutions.<ref name="venkataraman92">{{cite book |last=Venkataraman |first=G. |author-link=Ganeshan Venkataraman |url=https://books.google.com/books?id=HNSdDFOJ4wkC&pg=PA89 |title=Chandrasekhar and his limit |date=1992 |publisher=Universities Press |isbn=978-81-7371-035-3 |page=89 |archive-url=https://web.archive.org/web/20160811035848/https://books.google.com/books?id=HNSdDFOJ4wkC&pg=PA89 |archive-date=11 August 2016 |url-status=live}}</ref> His arguments were opposed by many of his contemporaries like Eddington and [[Lev Landau]], who argued that some yet unknown mechanism would stop the collapse.<ref>{{cite journal |last=Detweiler |first=S. |author-link=Steven Detweiler |date=1981 |title=Resource letter BH-1: Black holes |journal=[[American Journal of Physics]] |type=Paper |volume=49 |issue=5 |pages=394–400 |bibcode=1981AmJPh..49..394D |doi=10.1119/1.12686}}</ref> They were partially correct: a [[white dwarf]] slightly more massive than the Chandrasekhar limit will collapse into a [[neutron star]], which is itself stable.<ref>{{cite book |last1=Harpaz |first1=A. |date=1994 |title=Stellar evolution |url=https://books.google.com/books?id=kd4VEZv8oo0C&pg=PA105 |publisher=[[A K Peters, Ltd.|A K Peters]] |page=105 |isbn=978-1-56881-012-6 |url-status=live |archive-url=https://web.archive.org/web/20160811025449/https://books.google.com/books?id=kd4VEZv8oo0C&pg=PA105 |archive-date=11 August 2016}}</ref>

In 1939, based on Chandrasekhar's reasoning, [[Robert Oppenheimer]] and [[George Volkoff]] predicted that neutron stars above another mass limit, now known as the [[Tolman–Oppenheimer–Volkoff limit]], would collapse further, concluding that no law of physics was likely to intervene and stop at least some stars from collapsing to black holes.<ref name="OV1939">{{cite journal |last1=Oppenheimer |first1=J. R. |author-link1=J. Robert Oppenheimer |last2=Volkoff |first2=G. M. |author-link2=George Volkoff |date=1939 |title=On Massive Neutron Cores |journal=[[Physical Review]] |volume=55 |issue=4 |pages=374–381 |doi=10.1103/PhysRev.55.374|bibcode=1939PhRv...55..374O}}</ref> Their original calculations, based on the [[Pauli exclusion principle]], gave it as {{Solar mass|0.7}}. Subsequent consideration of neutron-neutron repulsion mediated by the strong force raised the estimate to approximately {{Solar mass|1.5}} to {{Solar mass|3.0}}.<ref name="Bombaci">{{cite journal |first=I. |last=Bombaci |date=1996 |title=The Maximum Mass of a Neutron Star |journal=[[Astronomy and Astrophysics]] |volume=305 |pages=871–877 |bibcode=1996A&A...305..871B}}</ref> Observations of the neutron star merger [[GW170817]], which is thought to have generated a black hole shortly afterward, have refined the TOV limit estimate to ~{{Solar mass|2.17}}.<ref name="Cho2018">{{cite journal |last=Cho |first=A. |date=16 February 2018 |title=A weight limit emerges for neutron stars |journal=Science |type=News |volume=359 |issue=6377 |pages=724–725 |bibcode=2018Sci...359..724C |doi=10.1126/science.359.6377.724 |pmid=29449468}}</ref><ref name="Margalit2017">{{cite journal |last1=Margalit |first1=B. |last2=Metzger |first2=B. D. |date=1 December 2017 |title=Constraining the Maximum Mass of Neutron Stars from Multi-messenger Observations of GW170817 |journal=[[The Astrophysical Journal Letters]] |type=Article |volume=850 |issue=2 |page=L19 |arxiv=1710.05938 |bibcode=2017ApJ...850L..19M |doi=10.3847/2041-8213/aa991c |s2cid=119342447 |doi-access=free}}</ref><ref name="Shibata2017">{{cite journal |vauthors=Shibata M, Fujibayashi S, Hotokezaka K, Kiuchi K, Kyutoku K, Sekiguchi Y, Tanaka M |date=22 December 2017 |title=Modeling GW170817 based on numerical relativity and its implications |journal=[[Physical Review D]] |type=Article |volume=96 |issue=12 |arxiv=1710.07579 |bibcode=2017PhRvD..96l3012S |doi=10.1103/PhysRevD.96.123012 |s2cid=119206732 |article-number=123012}}</ref><ref name="Ruiz2018">{{cite journal |vauthors=Ruiz M, [[Stuart L. Shapiro|Shapiro SL]], Tsokaros A |date=11 January 2018 |title=GW170817, general relativistic magnetohydrodynamic simulations, and the neutron star maximum mass |journal=[[Physical Review D]] |type=Rapid communication |volume=97 |issue=2 |arxiv=1711.00473 |bibcode=2018PhRvD..97b1501R |doi=10.1103/PhysRevD.97.021501 |pmc=6036631 |pmid=30003183 |article-number=021501}}</ref><ref name="Rezzolla2018">{{cite journal |vauthors=[[Luciano Rezzolla|Rezzolla L]], Most ER, Weih LR |date=9 January 2018 |title=Using Gravitational-wave Observations and Quasi-universal Relations to Constrain the Maximum Mass of Neutron Stars |journal=[[The Astrophysical Journal Letters]] |type=Article |volume=852 |issue=2 |page=L25 |arxiv=1711.00314 |bibcode=2018ApJ...852L..25R |doi=10.3847/2041-8213/aaa401 |s2cid=119359694 |doi-access=free}}</ref>

Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped.<ref name="OV1939" />{{rp |page=380–381 |quote=There would then seem to be only two answers possible to the question of the behavior of very massive stars: either the equation of state we have used so far fails to describe the behavior of highly condensed matter that the conclusions reached above are qualitatively misleading, or the star will continue to contract indefinitely, never reaching equilibrium.}} This is a valid point of view for external observers, but not for infalling observers.<ref name="Ruffini-2011" /> [[John Archibald Wheeler|John Wheeler]] later described black holes viewed from an external reference frame as "frozen stars" because an outside observer would see the surface of the star frozen in time due to gravitational time dilation, never to fully collapse.<ref name="Ruffini-2011">{{cite journal |last1=Ruffini |first1=R. |author-link1=Remo Ruffini |last2=Wheeler |first2=J. A. |author-link2=John Archibald Wheeler |date=1971 |title=Introducing the black hole |url=http://authors.library.caltech.edu/14972/1/Ruffini2009p1645Phys_Today.pdf |journal=[[Physics Today]] |type=Feature article |volume=24 |issue=1 |pages=30–41 |bibcode=1971PhT....24a..30R |doi=10.1063/1.3022513 |archive-url=https://web.archive.org/web/20110725133758/http://authors.library.caltech.edu/14972/1/Ruffini2009p1645Phys_Today.pdf |archive-date=25 July 2011 |access-date=5 December 2009}}</ref>

Also in 1939, Einstein attempted to prove that black holes were impossible in his publication "On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses", using his theory of general relativity to defend his argument.<ref name="Bernstein-2007">{{cite magazine |last=Bernstein |first=Jeremy |author-link=Jeremy Bernstein |date=2007 |title=The Reluctant Father of Black Holes |url=https://www.scientificamerican.com/article/the-reluctant-father-of-black-holes-2007-04/ |url-access=subscription |access-date=3 August 2023 |magazine=[[Scientific American]] |pages=4–11 |language=en |volume=17 |doi=10.1038/scientificamerican0407-4sp}}</ref> Months later, Oppenheimer and his student [[Hartland Snyder]] provided the [[Oppenheimer–Snyder model]] in their paper "On Continued Gravitational Contraction",<ref>{{cite journal |last1=Oppenheimer |first1=J.R. |author-link=J. Robert Oppenheimer |last2=Snyder |first2=H. |author-link2=Hartland Snyder |year=1939 |title=On Continued Gravitational Contraction |journal=[[Physical Review]] |type=Highlighted article |volume=56 |issue=5 |pages=455–459 |bibcode=1939PhRv...56..455O |doi=10.1103/PhysRev.56.455 |doi-access=free}}</ref> which predicted the existence of black holes. In the paper, which made no reference to Einstein's recent publication, Oppenheimer and Snyder used Einstein's own theory of general relativity to show the conditions on how a black hole could develop, for the first time in contemporary physics.<ref name="Bernstein-2007" />

In 1958, [[David Finkelstein]] identified the Schwarzschild surface as an event horizon, calling it "a perfect unidirectional membrane: causal influences can cross it in only one direction". In this sense, events that occur inside of the black hole cannot affect events that occur outside of the black hole.<ref>{{cite journal |last=Finkelstein |first=D. |author-link1=David Finkelstein |date=1958 |title=Past-Future Asymmetry of the Gravitational Field of a Point Particle |journal=[[Physical Review]] |type=Article |volume=110 |issue=4 |pages=965–967 |bibcode=1958PhRv..110..965F |doi=10.1103/PhysRev.110.965}}</ref> Finkelstein created a new [[Kruskal–Szekeres coordinates|reference frame]] to include the point of view of infalling observers.<ref name=Bartusiak/>{{rp|103}} Finkelstein's solution extended the Schwarzschild solution for the future of observers falling into a black hole. A similar concept had already been found by [[Martin Kruskal]], but its significance had not been fully understood at the time.<ref name=Bartusiak/>{{rp|103}}

=== Golden age ===
[[File:BH-JPL-A&A1979.jpg|thumb|The first simulated image of a black hole, created by [[Jean-Pierre Luminet]] in 1978 and featuring the characteristic shadow, [[photon sphere]], and [[gravitational lensing|lensed]] [[accretion disk]]. The disk is brighter on one side due to the [[Doppler beaming]].<ref>{{cite journal |last=Luminet |first=J.-P. |date=May 1979 |title=Image of a spherical black hole with thin accretion disk. |url=https://ui.adsabs.harvard.edu/abs/1979A&A....75..228L/abstract |journal=Astronomy and Astrophysics |language=en |volume=75 |pages=228–235 |bibcode=1979A&A....75..228L |issn=0004-6361}}</ref><ref>{{cite web |author=French National Centre for Scientific Research |title=First ever image of a black hole: a CNRS researcher had simulated it as early as 1979 |url=https://www.cnrs.fr/en/press/first-ever-image-black-hole-cnrs-researcher-had-simulated-it-early-1979 |website=CNRS |date=10 April 2019 |access-date=18 June 2025}}</ref>]]

The era from the mid-1960s to the mid-1970s was the "golden age of black hole research", when general relativity and black holes became mainstream subjects of research.<ref>{{cite book |last1=Thorne |first1=Kip |author-link=Kip Thorne |url=https://books.google.com/books?id=yLy4b61rfPwC |title=The future of theoretical physics and cosmology: celebrating Stephen Hawking's 60th birthday |publisher=[[Cambridge University Press]] |year=2003 |isbn=0-521-82081-2 |veditors=Shellard ES, [[Gary Gibbons|Gibbons GW]], Rankin SJ |page=74 |chapter=5. Warping spacetime}}</ref><ref>{{cite book |last=Thorne |first=Kip |author-link=Kip Thorne |title=Black Holes and Time Warps: Einstein's Outrageous Legacy (Commonwealth Fund Book Program) |date=1995 |publisher=W. W. Norton & Company, Incorporated |isbn=978-0-393-31276-8 |edition=1 |series=Commonwealth Fund Book Program Series |location=Erscheinungsort nicht ermittelbar}}</ref>{{rp|p=258}}

In this period, more general black hole solutions were found. In 1963, [[Roy Kerr]] found [[Kerr metric|the exact solution]] for a [[rotating black hole]].<ref>{{cite book |last=Kerr |first=R. P. |author-link=Roy Kerr |title=The Kerr Spacetime |date=2009 |publisher=[[Cambridge University Press]] |isbn=978-0-521-88512-6 |editor1-last=Wiltshire |editor1-first=D. L. |chapter=Discovering the Kerr and Kerr-Schild metrics |bibcode=2007arXiv0706.1109K |editor2-last=Visser |editor2-first=M. |editor3-last=Scott |editor3-first=S. M. |arxiv=0706.1109}}</ref><ref>{{cite web |last=Hooper |first=Dan |author-link=Dan Hooper |date=27 December 2019 |title=The Discovery of Black Holes: From Theory to Actuality |url=https://www.wondriumdaily.com/the-discovery-of-black-holes-from-theory-to-actuality/ |archive-url=https://web.archive.org/web/20220925103539/https://www.wondriumdaily.com/the-discovery-of-black-holes-from-theory-to-actuality/ |archive-date=25 September 2022 |access-date=29 June 2022 |website=Wondrium Daily |publisher=[[The Teaching Company]] |language=en-US |publication-place=Virginia, United States}}</ref> Two years later, [[Ezra T. Newman|Ezra Newman]] found the [[Rotational symmetry#Rotational symmetry with respect to any angle|cylindrically symmetric]] solution for a black hole that is both rotating and [[electrically charged]].<ref>{{cite journal |display-authors=1 |vauthors=[[Ezra T. Newman|Newman ET]], Couch E, Chinnapared K, Exton A, Prakash A, Torrence R |date=1965 |title=Metric of a Rotating, Charged Mass |journal=[[Journal of Mathematical Physics]] |type=Research article |volume=6 |issue=6 |page=918 |bibcode=1965JMP.....6..918N |doi=10.1063/1.1704351}}</ref>

In 1967, [[Werner Israel]] found that the Schwarzschild solution was the only possible solution for a nonspinning, uncharged black hole, and couldn't have any additional parameters. In that sense, a Schwarzschild black hole would be defined by its [[mass]] alone, and any two Schwarzschild black holes with the same mass would be identical.<ref>{{cite journal |last=Israel |first=W. |author-link=Werner Israel |date=1967 |title=Event Horizons in Static Vacuum Space-Times |journal=[[Physical Review]] |type=Article |volume=164 |issue=5 |page=1776 |bibcode=1967PhRv..164.1776I |doi=10.1103/PhysRev.164.1776}}</ref> Israel later found that Reissner-Nordstrom black holes were only defined by their mass and electric charge, while [[Brandon Carter]] discovered that Kerr black holes only had two [[degrees of freedom]], mass and [[angular momentum|spin]].<ref>{{cite journal |last=Carter |first=B. |author-link1=Brandon Carter |date=1971 |title=Axisymmetric Black Hole Has Only Two Degrees of Freedom |department=Elementary Particles and Fields |journal=[[Physical Review Letters]] |type=Letter |volume=26 |issue=6 |page=331 |bibcode=1971PhRvL..26..331C |doi=10.1103/PhysRevLett.26.331}}</ref><ref>{{cite book |last=Carter |first=B. |author-link1=Brandon Carter |date=1977 |chapter=The vacuum black hole uniqueness theorem and its conceivable generalisations |title=Proceedings of the 1st Marcel Grossmann meeting on general relativity |pages=243–254 }}</ref> Together, these findings became known as the [[no-hair theorem]], which states that a stationary black hole is completely described by the three parameters of the [[Kerr–Newman metric]]: mass, angular momentum, and electric charge.<ref name="HeuslerNoHair" />

At first, it was suspected that the strange mathematical singularities found in each of the black hole solutions only appeared due to the assumption that a black hole would be perfectly [[Rotational symmetry#Rotational symmetry with respect to any angle|spherically symmetric]], and therefore the singularities would not appear in generic situations where black holes would not necessarily be symmetric. This view was held in particular by [[Vladimir A. Belinsky|Vladimir Belinski]], [[Isaak Markovich Khalatnikov|Isaak Khalatnikov]], and [[Evgeny Lifshitz]], who tried to prove that no singularities appear in generic solutions, although they would later reverse their positions.<ref>{{Cite journal |last1=Penrose |first1=Roger |author-link=Roger Penrose |date=1996 |title=Chandrasekhar, black holes, and singularities |journal=[[Journal of Astrophysics and Astronomy]] |type=Article |volume=17 |issue=3–4 |pages=213–231 |bibcode=1996JApA...17..213P |doi=10.1007/BF02702305}}</ref> However, in 1965, [[Roger Penrose]] proved that general relativity without quantum mechanics requires that singularities appear in all black holes.<ref name="penrose1965">{{cite journal |last1=Penrose |first1=R. |author-link1=Roger Penrose |date=1965 |title=Gravitational Collapse and Space-Time Singularities |url=http://pdfs.semanticscholar.org/faad/1f4358fddf70df2e00c0a290b7e4501c27de.pdf |url-status=live |journal=[[Physical Review Letters]] |volume=14 |issue=3 |page=57 |bibcode=1965PhRvL..14...57P |doi=10.1103/PhysRevLett.14.57 |s2cid=116755736 |archive-url=https://web.archive.org/web/20201011221750/http://pdfs.semanticscholar.org/faad/1f4358fddf70df2e00c0a290b7e4501c27de.pdf |archive-date=11 October 2020 |doi-access=free}}</ref><ref>{{cite journal |last1=Ford |first1=L. H. |date=2003 |title=The Classical Singularity Theorems and Their Quantum Loopholes |journal=[[International Journal of Theoretical Physics]] |volume=42 |issue=6 |pages=1219–1227 |doi=10.1023/A:1025754515197 |arxiv=gr-qc/0301045 |bibcode=2003gr.qc.....1045F |s2cid=14404560}}</ref> Shortly afterwards, Hawking generalized Penrose's solution to find that in all but a few physically infeasible scenarios, a cosmological [[Big Bang]] singularity is inevitable unless quantum gravity intervenes.<ref>{{Cite journal |title=The Occurrence of Singularities in Cosmology |journal=Proceedings of the Royal Society A |last=Hawking |first=Stephen |date=18 October 1966 |url=https://www.jstor.org/stable/pdf/2415489.pdf |volume=294 |issue=1439 |via=JSTOR |author-link=Stephen Hawking |pages=511–521 |doi=10.1098/rspa.1966.0221 |jstor=2415489 |bibcode=1966RSPSA.294..511H }}</ref> For his work, Penrose received half of the 2020 [[Nobel Prize in Physics]], Hawking having died in 2018.<ref>{{cite web|title=The Nobel Prize in Physics 2020|url=https://www.nobelprize.org/prizes/physics/2020/summary/|access-date=8 October 2020|website=NobelPrize.org|archive-date=24 April 2021|archive-url=https://web.archive.org/web/20210424115309/https://www.nobelprize.org/prizes/physics/2020/summary/|url-status=live}}</ref>

Astronomical observations also made great strides during this era. In 1967, [[Antony Hewish]] and [[Jocelyn Bell Burnell]] discovered [[pulsar]]s<ref>{{cite journal |last1=Hewish |first1=A. |author-link1=Antony Hewish |last2=Bell |first2=S. J. |author-link2=Jocelyn Bell Burnell |last3=Pilkington |first3=J. D. H. |last4=Scott |first4=P. F. |last5=Collins |first5=R. A. |display-authors=1 |date=1968 |title=Observation of a Rapidly Pulsating Radio Source |journal=[[Nature (journal)|Nature]] |volume=217 |issue=5130 |pages=709–713 |doi=10.1038/217709a0|bibcode=1968Natur.217..709H|s2cid=4277613 }}</ref><ref>{{cite journal |last1=Pilkington |first1=J. D. H. |last2=Hewish |first2=A. |author-link2=Antony Hewish |last3=Bell |first3=S. J. |author-link3=Jocelyn Bell Burnell |last4=Cole |first4=T. W. |display-authors=1 |date=1968 |title=Observations of some further Pulsed Radio Sources |journal=[[Nature (journal)|Nature]] |volume=218 |issue=5137 |pages=126–129 |doi=10.1038/218126a0|bibcode=1968Natur.218..126P|s2cid=4253103 }}</ref> and by 1969, these were shown to be rapidly rotating neutron stars.<ref name="araa8_265">{{cite journal |last=Hewish |first=A. |author-link1=Antony Hewish |date=1970 |title=Pulsars |journal=[[Annual Review of Astronomy and Astrophysics]] |volume=8 |issue=1 |pages=265–296 |bibcode=1970ARA&A...8..265H |doi=10.1146/annurev.aa.08.090170.001405}}</ref> Until that time, neutron stars, like black holes, were regarded as just theoretical curiosities, but the discovery of pulsars showed their physical relevance and spurred a further interest in all types of compact objects that might be formed by gravitational collapse.<ref>{{cite web |url=https://www.smithsonianmag.com/science-nature/Fifty-years-ago-grad-students-discovery-changed-course-astrophysics-180968288/ |title=Fifty Years Ago, a Grad Student's Discovery Changed the Course of Astrophysics |date=28 February 2018 |access-date=22 December 2023 |website=Smithsonian Magazine |last=Boissoneault |first=Lorraine}}</ref> Based on observations in [[Royal Greenwich Observatory|Greenwich]] and [[David Dunlap Observatory|Toronto]] in the early 1970s, [[Cygnus X-1]], a galactic [[X-ray]] source discovered in 1964, became the first astronomical object commonly accepted to be a black hole.<ref>{{citation | last=Rolston | first=Bruce | date=10 November 1997 | url=http://news.utoronto.ca/bin/bulletin/nov10_97/art4.htm | title=The First Black Hole | publisher=University of Toronto | access-date=11 March 2008 | archive-url = https://web.archive.org/web/20080307181205/http://www.news.utoronto.ca/bin/bulletin/nov10_97/art4.htm | archive-date = 7 March 2008 }}</ref><ref name="Shipman1975">{{citation | last1=Shipman | first1=H. L. | date=1975 | title=The implausible history of triple star models for Cygnus&nbsp;X-1 Evidence for a black hole | journal=Astrophysical Letters | volume=16 | issue=1 | pages=9–12 | bibcode=1975ApL....16....9S | doi=10.1016/S0304-8853(99)00384-4 | last2=Yu | first2=Z | last3=Du | first3=Y.W }}</ref>

Work by [[James Bardeen]], [[Jacob Bekenstein]], Carter, and Hawking in the early 1970s led to the formulation of [[black hole thermodynamics]].<ref>{{cite journal |last1=Bardeen |first1=J. M. |author-link1=James M. Bardeen |last2=Carter |first2=B. |author-link2=Brandon Carter |last3=Hawking |first3=S. W. |author-link3=Stephen Hawking |date=1973 |title=The four laws of black hole mechanics |journal=[[Communications in Mathematical Physics]] |volume=31 |issue=2 |pages=161–170 |doi=10.1007/BF01645742 |mr=0334798 |zbl=1125.83309 |bibcode=1973CMaPh..31..161B |s2cid=54690354 |url=http://projecteuclid.org/euclid.cmp/1103858973 |access-date=4 June 2021 |archive-date=16 May 2020 |archive-url=https://web.archive.org/web/20200516211604/https://projecteuclid.org/euclid.cmp/1103858973 |url-status=live }}</ref> These laws describe the behaviour of a black hole in close analogy to the [[laws of thermodynamics]] by relating mass to energy, area to [[entropy]], and [[surface gravity]] to [[temperature]]. The analogy was completed when Hawking, in 1974, showed that [[quantum field theory]] implies that black holes should radiate like a [[black body]] with a temperature proportional to the surface gravity of the black hole, predicting the effect now known as [[Hawking radiation]].<ref name=Hawking1974 />

=== Modern research and observation ===
The first strong evidence for black holes came from combined X-ray and optical observations of [[Cygnus X-1]] in 1972.<ref>{{Cite journal |last1=Remillard |first1=Ronald A. |last2=McClintock |first2=Jeffrey E. |date=22 September 2006 |title=X-Ray Properties of Black-Hole Binaries |url=https://www.annualreviews.org/content/journals/10.1146/annurev.astro.44.051905.092532 |journal=Annual Review of Astronomy and Astrophysics |language=en |volume=44 |issue=<!--none--> |pages=49–92 |doi=10.1146/annurev.astro.44.051905.092532 |arxiv=astro-ph/0606352 |bibcode=2006ARA&A..44...49R |issn=0066-4146}}</ref> The x-ray source, located in the [[Cygnus (constellation)|Cygnus]] constellation, was discovered through a survey by two [[suborbital rocket]]s,  as the blocking of x-rays by [[Earth's atmosphere]] makes it difficult to detect them from the ground.<ref>{{cite book | first=Friedman | last=Herbert | date=2002 | chapter=From the ionosphere to high energy astronomy&nbsp;– a personal experience | title=The Century of Space Science | publisher=Springer | isbn=0-7923-7196-8 }}</ref><ref>{{cite journal | last1=Liu | first1=C. Z. | last2=Li | first2=T. P. | title=X-Ray Spectral Variability in Cygnus&nbsp;X-1 | journal=The Astrophysical Journal | year=2004 | volume=611 | issue=2 | pages=1084–1090 | doi=10.1086/422209 | bibcode=2004ApJ...611.1084L|arxiv = astro-ph/0405246 | s2cid=208868049 }}</ref><ref name="bbcf65">{{cite journal | last1=Bowyer | first1=S. | last2=Byram | first2=E. T. | last3=Chubb | first3=T. A. | last4=Friedman | first4=H. | date=1965 | title=Cosmic X-ray Sources | journal=Science | volume=147 | issue=3656 | pages=394–398 | doi=10.1126/science.147.3656.394 | pmid=17832788 | bibcode=1965Sci...147..394B | s2cid=206565068 }}</ref> Unlike stars or pulsars, Cygnus X-1 was not associated with any prominent radio or optical source.<ref name="bbcf65" /><ref>{{Cite journal |last1=Maron |first1=O. |last2=Kijak |first2=J. |last3=Kramer |first3=M. |last4=Wielebinski |first4=R. |title=Pulsar spectra of radio emission |journal=Astronomy and Astrophysics Supplement Series |date=2000 |volume=147 |issue=2 |pages=195–203 |doi=10.1051/aas:2000298 |arxiv=astro-ph/0010233 |bibcode=2000A&AS..147..195M }}</ref> In 1972, [[Betty Louise Turtle|Louise Webster]], [[Paul Murdin]], and, independently, [[Charles Thomas Bolton]], found that Cygnus X-1 was actually in a [[X-ray binary|binary system]] with the [[supergiant star]] HDE 226868. Using the [[astronomical spectroscopy|emission patterns]] of the visible star, both research teams found that the mass of Cygnus X-1 was likely too large to be a [[white dwarf]] or neutron star, indicating that it was probably a black hole.<ref name=wm72>{{cite journal | last1=Webster | first1=B. Louise | last2=Murdin | first2=Paul | date=1972 | title=Cygnus&nbsp;X-1—a Spectroscopic Binary with a Heavy Companion? | journal=Nature | volume=235 | issue=5332 | pages=37–38 | doi=10.1038/235037a0 | bibcode = 1972Natur.235...37W | s2cid=4195462 }}</ref><ref name=bolton72>{{cite journal | last=Bolton | first=C. T. | date=1972 | title=Identification of Cygnus&nbsp;X-1 with HDE&nbsp;226868 | journal=Nature | volume=235 | issue=5336 | pages=271–273 | doi=10.1038/235271b0 | bibcode = 1972Natur.235..271B | s2cid=4222070 }}</ref> Further research strengthened their hypothesis.<ref name="rolston1997">{{cite web | last=Rolston | first=Bruce | date=10 November 1997 | url=http://news.utoronto.ca/bin/bulletin/nov10_97/art4.htm | title=The First Black Hole | publisher=University of Toronto | access-date=11 March 2008 | archive-url = https://web.archive.org/web/20080307181205/http://www.news.utoronto.ca/bin/bulletin/nov10_97/art4.htm | archive-date = 7 March 2008 }}</ref><ref>{{cite journal | last1=Shipman | first1=H. L. | date=1975 | title=The implausible history of triple star models for Cygnus&nbsp;X-1 Evidence for a black hole | journal=Astrophysical Letters | volume=16 | issue=1 | pages=9–12 | bibcode=1975ApL....16....9S | doi=10.1016/S0304-8853(99)00384-4 | last2=Yu | first2=Z. | last3=Du | first3=Y. W. }}</ref>

While Cygnus X-1, a [[stellar-mass black hole]], was generally accepted by the scientific community as a black hole by the end of 1973,<ref name="rolston1997" /> it would be decades before a [[supermassive black hole]] would gain the same broad recognition. Although, as early as the 1960s, physicists such as [[Donald Lynden-Bell]] and [[Martin Rees]] had suggested that powerful [[quasars]] in the center of galaxies were powered by [[accretion (astrophysics)|accreting]] supermassive black holes, little observational proof existed at the time.<ref>{{Cite journal |last1=Lynden-Bell |first1=D. |title=Galactic Nuclei as Collapsed Old Quasars |journal=Nature |date=1969 |volume=223 |issue=5207 |pages=690–694 |doi=10.1038/223690a0 |bibcode=1969Natur.223..690L }}</ref><ref>{{Cite journal |last1= Rees|first1= Martin J.|title= Black Hole Models for Active Galactic Nuclei|journal= Annual Review of Astronomy and Astrophysics|date= 1984|volume= 22|pages= 471–506|doi=10.1146/annurev.aa.22.090184.002351|bibcode= 1984ARA&A..22..471R}}</ref> However, the [[Hubble Space Telescope]], launched decades later, found that supermassive black holes were not only present in these [[active galactic nuclei]], but that supermassive black holes in the center of galaxies were ubiquitous: Almost every galaxy had a supermassive black hole at its center, many of which were quiescent.<ref name="ff05">{{Cite journal |last1=Ferrarese |first1=Laura |last2=Ford |first2=Holland |title=Supermassive Black Holes in Galactic Nuclei: Past, Present and Future Research |journal=Space Science Reviews |date=2005 |volume=116 |issue=3–4 |pages=523–624 |doi=10.1007/s11214-005-3947-6 |arxiv=astro-ph/0411247 |bibcode=2005SSRv..116..523F }}</ref><ref name="peterson14">{{Cite journal |last1=Peterson |first1=Bradley M. |title=Measuring the Masses of Supermassive Black Holes |journal=Space Science Reviews |date=2014 |volume=183 |issue=1–4 |pages=253–275 |doi=10.1007/s11214-013-9987-4 |bibcode=2014SSRv..183..253P }}</ref> In 1999, [[David Merritt]] proposed the [[M–sigma relation]], which related the [[dispersion (statistics)|dispersion]] of the [[velocity]] of matter in the center [[galactic bulge|bulge]] of a galaxy to the mass of the supermassive black hole at its core.<ref>{{cite conference | first = David | last = Merritt | author-link = David Merritt | editor1-first = F. | editor1-last = Combes | editor2-first = G. A. | editor2-last = Mamon | editor3-first = V. | editor3-last = Charmandaris | title = Black holes and galaxy evolution | volume = 197 | book-title = Dynamics of Galaxies: from the Early Universe to the Present | publisher = [[Astronomical Society of the Pacific]] | pages = [https://archive.org/details/xvthiapmeetingdy0197iapm/page/221 221–232] | date = 1999 | isbn = 978-1-58381-024-8 | bibcode = 2000ASPC..197..221M | arxiv = astro-ph/9910546 | url = https://archive.org/details/xvthiapmeetingdy0197iapm/page/221 }}</ref> Subsequent studies confirmed this correlation.<ref>{{Cite journal |last1=Tremaine |first1=Scott |last2=Gebhardt |first2=Karl |last3=Bender |first3=Ralf |last4=Bower |first4=Gary |last5=Dressler |first5=Alan |last6=Faber |first6=S. M. |last7=Filippenko |first7=Alexei V. |last8=Green |first8=Richard |last9=Grillmair |first9=Carl |last10=Ho |first10=Luis C. |last11=Kormendy |first11=John |last12=Lauer |first12=Tod R. |last13=Magorrian |first13=John |last14=Pinkney |first14=Jason |last15=Richstone |first15=Douglas |title=The Slope of the Black Hole Mass versus Velocity Dispersion Correlation |journal=The Astrophysical Journal |date=2002 |volume=574 |issue=2 |pages=740–753 |doi=10.1086/341002 |arxiv=astro-ph/0203468 |bibcode=2002ApJ...574..740T }}</ref><ref>{{Cite journal |last1=Ferrarese |first1=Laura |last2=Merritt |first2=David |title=A Fundamental Relation between Supermassive Black Holes and Their Host Galaxies |journal=The Astrophysical Journal |date=2000 |volume=539 |issue=1 |pages=L9–L12 |doi=10.1086/312838 |arxiv=astro-ph/0006053 |bibcode=2000ApJ...539L...9F }}</ref><ref>{{Cite journal |last1=Nelson |first1=Charles H. |last2=Green |first2=Richard F. |last3=Bower |first3=Gary |last4=Gebhardt |first4=Karl |last5=Weistrop |first5=Donna |title=The Relationship Between Black Hole Mass and Velocity Dispersion in Seyfert 1 Galaxies |journal=The Astrophysical Journal |date=2004 |volume=615 |issue=2 |pages=652–661 |doi=10.1086/424657 |arxiv=astro-ph/0407383 |bibcode=2004ApJ...615..652N }}</ref> Around the same time, based on telescope observations of the velocities of stars at the center of the Milky Way galaxy, independent work groups led by [[Andrea Ghez]] and [[Reinhard Genzel]] concluded that the compact [[astronomical radio source|radio source]] in the center of the galaxy, [[Sagittarius A*]], was likely a supermassive black hole.<ref>{{Cite journal |last1=Genzel |first1=R. |last2=Eckart |first2=A. |last3=Ott |first3=T. |last4=Eisenhauer |first4=F. |title=On the nature of the dark mass in the centre of the Milky Way |journal=Monthly Notices of the Royal Astronomical Society |date=1997 |volume=291 |pages=219–234 |doi=10.1093/mnras/291.1.219 |doi-access=free }}</ref><ref>{{Cite journal |last1=Ghez |first1=A. M. |last2=Klein |first2=B. L. |last3=Morris |first3=M. |last4=Becklin |first4=E. E. |title=High Proper-Motion Stars in the Vicinity of Sagittarius A*: Evidence for a Supermassive Black Hole at the Center of Our Galaxy |journal=The Astrophysical Journal |date=1998 |volume=509 |issue=2 |pages=678–686 |doi=10.1086/306528 |arxiv=astro-ph/9807210 |bibcode=1998ApJ...509..678G }}</ref> In 2020, Ghez and Genzel won the [[Nobel Prize in Physics]] for their prediction.<ref>{{Cite web |title=Oxford Mathematician Roger Penrose jointly wins the Nobel Prize in Physics |url=https://www.ox.ac.uk/news/2020-10-06-oxford-mathematician-roger-penrose-jointly-wins-nobel-prize-physics |date=6 October 2020 |access-date=20 October 2025 |website=University of Oxford}}</ref><ref>{{Cite web |title=2020 Nobel Prize in Physics |url=https://www.aps.org/archives/publications/apsnews/202011/nobel-physics.cfm |last=Poffenberger |first=Leah |access-date=20 October 2025 |website=American Physical Society}}</ref>

[[File:LIGO measurement of gravitational waves.svg|thumb |The first detection of gravitational waves, imaged by LIGO observatories in [[Hanford Site|Hanford Site, Washington]] and [[Livingston, Louisiana]]]]

On 11 February 2016, the [[LIGO Scientific Collaboration]] and [[Virgo interferometer|Virgo Collaboration]] announced the [[first observation of gravitational waves|first direct detection]] of [[gravitational wave]]s, named GW150914, representing the first observation of a [[black hole merger]].<ref name="PRL-20160211" /> At the time of the merger, the black holes were approximately 1.4 billion [[light-years]] away from Earth and had masses of 30 and 35 solar masses.<ref name="ligovirgo16">{{Cite journal|arxiv=1606.01210 |title=An improved analysis of GW150914 using a fully spin-precessing waveform model |journal=Physical Review X |volume=6 |issue=4 |article-number=041014 |author=The LIGO Scientific Collaboration and The Virgo Collaboration |doi=10.1103/PhysRevX.6.041014 |year=2016 |bibcode=2016PhRvX...6d1014A |s2cid=18217435 }}</ref>{{Rp|6}} The mass of the resulting black hole was approximately 62 solar masses, with an additional three solar masses [[mass-energy equivalence|radiated away]] as gravitational waves.<ref name="ligovirgo16" /><ref>{{cite journal |collaboration=LIGO Scientific Collaboration and Virgo Collaboration |last1=Abbott |first1=Benjamin P. |title=Observation of Gravitational Waves from a Binary Black Hole Merger |journal=[[Phys. Rev. Lett.]] |volume=116 |issue=6 |article-number=061102 |year=2016 |doi=10.1103/PhysRevLett.116.061102 |arxiv=1602.03837 |bibcode=2016PhRvL.116f1102A |pmid=26918975|s2cid=124959784}}
* {{cite web |title=Observation of Gravitational Waves from a Binary Black Hole Merger |website=LIGO Scientific Collaboration |url=https://www.ligo.caltech.edu/system/media_files/binaries/301/original/detection-science-summary.pdf}}</ref> The [[Laser Interferometer Gravitational-Wave Observatory]] (LIGO) detected the gravitational waves by using two mirrors spaced four kilometers apart to measure microscopic changes in length.<ref>{{cite web |title=Facts |url=https://www.ligo.caltech.edu/page/facts |website=LIGO |quote=This is equivalent to measuring the distance from Earth to the nearest star to an accuracy smaller than the width of a human hair! |access-date=24 August 2017 |archive-url=https://web.archive.org/web/20170704030142/https://www.ligo.caltech.edu/page/facts |archive-date=4 July 2017 }} (that is, to [[Proxima Centauri]] at {{val|4.0208|e=13|u=km}}).</ref> In 2017, [[Rainer Weiss]], [[Kip Thorne]], and [[Barry Barish]], who had spearheaded the project, were awarded the Nobel Prize in Physics for their work.<ref>{{cite web |title=The Nobel Prize in Physics 2017 |publisher=Nobel Foundation |url=https://www.nobelprize.org/nobel_prizes/physics/laureates/2017/press.html }}</ref> Since the initial discovery in 2015, hundreds more gravitational waves have been observed by LIGO and another interferometer, [[Virgo interferometer|Virgo]].<ref>{{Cite web |title=LIGO-Virgo-KAGRA Announce the 200th Gravitational Wave Detection of O4! |url=https://www.ligo.caltech.edu/news/ligo20250320 |last=Burtnyk |first=Kimberly |date=20 March 2025 |access-date=22 October 2025 |website=LIGO Caltech}}</ref>

[[File:Black hole - Messier 87.jpg|thumb |Image by the [[Event Horizon Telescope]] of the supermassive black hole in the center of [[Messier 87]]]]

On 10 April 2019, the first direct image of a black hole and its vicinity was published, following observations made by the [[Event Horizon Telescope]] (EHT) in 2017 of the supermassive black hole in [[Messier 87]]'s [[Galactic Center|galactic centre]].<ref name="APJL-20190410">{{cite journal|last1=Event Horizon Telescope|first1=The|author-link1=Event Horizon Telescope|date=2019|title=First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole|journal=[[The Astrophysical Journal]]|volume=875|page=L1|arxiv=1906.11238|bibcode=2019ApJ...875L...1E|doi=10.3847/2041-8213/ab0ec7|number=1|s2cid=145906806 |doi-access=free }}</ref><ref name="BoumanJohnson2016">{{cite book |last1=Bouman |first1=Katherine L. |title=2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) |author-link1=Katie Bouman |last2=Johnson |first2=Michael D. |last3=Zoran |first3=Daniel |last4=Fish |first4=Vincent L. |last5=Doeleman |first5=Sheperd S. |last6=Freeman |first6=William T. |chapter=Computational Imaging for VLBI Image Reconstruction |year=2016 |pages=913–922 |doi=10.1109/CVPR.2016.105 |hdl=1721.1/103077 |arxiv=1512.01413|isbn=978-1-4673-8851-1|s2cid=9085016 }}</ref><ref name="NYT-20190412">{{cite news |last=Gardiner |first=Aidan |title=When a Black Hole Finally Reveals Itself, It Helps to Have Our Very Own Cosmic Reporter – Astronomers announced Wednesday that they had captured the first image of a black hole. The Times's Dennis Overbye answers readers' questions.|url=https://www.nytimes.com/2019/04/12/reader-center/black-holes-dennis-overbye.html |archive-url=https://ghostarchive.org/archive/20220101/https://www.nytimes.com/2019/04/12/reader-center/black-holes-dennis-overbye.html |archive-date=1 January 2022 |url-access=limited |date=12 April 2018 |work=[[The New York Times]] |access-date=15 April 2019}}{{cbignore}}</ref> The observations were carried out by eight [[observatories]] in six geographical locations across four days and totaled five [[petabyte]]s of data.<ref>{{Cite web |title=How many telescopes are currently in the EHT network? |url=https://eventhorizontelescope.org/faq/how-many-telescopes-are-currently-network |access-date=22 October 2025 |website=Event Horizon Telescope}}</ref><ref>{{Cite web |title=How Scientists Captured the First Image of a Black Hole |url=https://www.jpl.nasa.gov/edu/resources/teachable-moment/how-scientists-captured-the-first-image-of-a-black-hole/ |last=Lutz |first=Ota |date=8 October 2024 |access-date=22 October 2025 |website=NASA.gov}}</ref><ref>{{Cite magazine |date=12 April 2019 |title=The M87 image will change our understanding of black holes, but why was the photo so hard to capture? |magazine=BBC Science Focus Magazine |last=Chown |first=Marcus |url=https://www.sciencefocus.com/space/m87-why-the-first-black-hole-photo-was-so-hard-to-capture |access-date=22 October 2025}}</ref> In 2022, the Event Horizon Telescope collaboration released an image of the black hole in the center of the Milky Way galaxy, Sagittarius A*; The data had been collected in 2017.<ref>{{Cite web |title=Astronomers Reveal First Image of the Black Hole at the Heart of Our Galaxy |url=https://eventhorizontelescope.org/blog/astronomers-reveal-first-image-black-hole-heart-our-galaxy |date=12 May 2022 |website=Event Horizon Telescope}}</ref> Detailed analysis of the motion of stars recorded by the [[Gaia (spacecraft)|Gaia mission]] produced  evidence in 2022<ref>{{Cite journal |last1=Chakrabarti |first1=Sukanya |last2=Simon |first2=Joshua D. |last3=Craig |first3=Peter A. |last4=Reggiani |first4=Henrique |last5=Brandt |first5=Timothy D. |last6=Guhathakurta |first6=Puragra |last7=Dalba |first7=Paul A. |last8=Kirby |first8=Evan N. |last9=Chang |first9=Philip |last10=Hey |first10=Daniel R. |last11=Savino |first11=Alessandro |last12=Geha |first12=Marla |last13=Thompson |first13=Ian B. |date=1 July 2023 |title=A Noninteracting Galactic Black Hole Candidate in a Binary System with a Main-sequence Star |journal=The Astronomical Journal |volume=166 |issue=1 |page=6 |doi=10.3847/1538-3881/accf21 |arxiv=2210.05003 |bibcode=2023AJ....166....6C |doi-access=free |issn=0004-6256}}</ref> and 2023<ref name="El-Badry">{{cite journal |last1=El-Badry |first1=Kareem |last2=Rix |first2=Hans-Walter |last3=Quataert |first3=Eliot |last4=Howard |first4=Andrew W. |last5=Isaacson |first5=Howard |last6=Fuller |first6=Jim |last7=Hawkins |first7=Keith |last8=Breivik |first8=Katelyn |last9=Wong |first9=Kaze W. K. |last10=Rodriguez |first10=Antonio C. |last11=Conroy |first11=Charlie |last12=Shahaf |first12=Sahar |last13=Mazeh |first13=Tsevi |last14=Arenou |first14=Frédéric |last15=Burdge |first15=Kevin B. |last16=Bashi |first16=Dolev |last17=Faigler |first17=Simchon |last18=Weisz |first18=Daniel R. |last19=Seeburger |first19=Rhys |last20=Monter |first20=Silvia Almada |last21=Wojno |first21=Jennifer |title=A Sun-like star orbiting a black hole  |journal=Monthly Notices of the Royal Astronomical Society |year=2023 |volume=518 |issue=1 |pages=1057–1085 |doi=10.1093/mnras/stac3140 |doi-access=free |arxiv=2209.06833 |bibcode=2023MNRAS.518.1057E }}</ref> of a black hole named [[Gaia BH1]] in a binary with a Sun-like star about {{convert|1,560|ly|pc|lk=on|abbr=off}} away. Gaia BH1 is currently the closest known black hole to Earth.<ref name="El-Badry2022">{{cite journal |last1=El-Badry |first1=Kareem |last2=Rix |first2=Hans-Walter |last3=Quataert |first3=Eliot |last4=Howard |first4=Andrew W. |last5=Isaacson |first5=Howard |last6=Fuller |first6=Jim |last7=Hawkins |first7=Keith |last8=Breivik |first8=Katelyn |last9=Wong |first9=Kaze W. K. |last10=Rodriguez |first10=Antonio C. |last11=Conroy |first11=Charlie |last12=Shahaf |first12=Sahar |last13=Mazeh |first13=Tsevi |last14=Arenou |first14=Frédéric |last15=Burdge |first15=Kevin B. |display-authors=2 |date=2 November 2022 |title=A Sun-like star orbiting a black hole |journal=[[Monthly Notices of the Royal Astronomical Society]] |volume=518 |issue=1 |pages=1057–1085 |arxiv=2209.06833 |doi=10.1093/mnras/stac3140 |doi-access=free |bibcode=2023MNRAS.518.1057E}}</ref><ref name="NOIRLab22">{{cite web |url=https://noirlab.edu/public/news/noirlab2227/ |title=Astronomers Discover Closest Black Hole to Earth |date=4 November 2022 |website=noirlab.edu |publisher=[[NOIRLab]] |access-date=4 November 2022}}</ref> Two more black holes have since been found from Gaia data, one in a binary with a [[red giant]]<ref name="elbadry23">{{Cite journal |last1=El-Badry |first1=Kareem |last2=Rix |first2=Hans-Walter |last3=Cendes |first3=Yvette |last4=Rodriguez |first4=Antonio C. |last5=Conroy |first5=Charlie |last6=Quataert |first6=Eliot |last7=Hawkins |first7=Keith |last8=Zari |first8=Eleonora |last9=Hobson |first9=Melissa |last10=Breivik |first10=Katelyn |last11=Rau |first11=Arne |last12=Berger |first12=Edo |last13=Shahaf |first13=Sahar |last14=Seeburger |first14=Rhys |last15=Burdge |first15=Kevin B. |date=1 February 2023 |title=A red giant orbiting a black hole |bibcode=2023MNRAS.521.4323E |arxiv=2302.07880 |journal=[[Monthly Notices of the Royal Astronomical Society]] |volume=521 |issue=3 |pages=4323–4348 |doi=10.1093/mnras/stad799|doi-access=free }}</ref> and the other in a binary with a [[Stellar classification#Class G|G-type]] star.<ref name="pmahc24" >{{Cite journal |last1=Panuzzo |first1=P. |last2=Mazeh | first2=T. | last3=Arenou | first3 = F.| last4=Holl | first4=B. | last5=Caffau | first5=E. |date=2024 |title=Discovery of a dormant 33 solar-mass black hole in pre-release Gaia astrometry |journal=The Astrophysical Journal |volume=686 |pages=L2 |doi=10.1051/0004-6361/202449763|arxiv=2404.10486|bibcode=2024A&A...686L...2G |doi-access=free }}</ref>

=== Etymology ===

In December 1967, a student reportedly suggested the phrase "black hole" at a lecture by [[John Archibald Wheeler|John Wheeler]]; Wheeler adopted the term for its brevity and "advertising value", and Wheeler's stature in the field ensured it quickly caught on,<ref name=Bartusiak/><ref>{{cite news |title=Pioneering Physicist John Wheeler Dies at 96 |url=https://www.scientificamerican.com/article/pioneering-physicist-john-wheeler-dies/ |access-date=27 November 2016 |work=[[Scientific American]] |url-status=live |archive-url=https://web.archive.org/web/20161128050759/https://www.scientificamerican.com/article/pioneering-physicist-john-wheeler-dies/ |archive-date=28 November 2016}}</ref> leading some to credit Wheeler with coining the phrase.<ref>{{cite news |last1=Overbye |first1=Dennis |title=John A. Wheeler, Physicist Who Coined the Term 'Black Hole,' Is Dead at 96 |url=https://www.nytimes.com/2008/04/14/science/14wheeler.html |access-date=27 November 2016 |work=[[The New York Times]] |date=14 April 2008 |url-status=live |archive-url=https://web.archive.org/web/20161122210005/http://www.nytimes.com/2008/04/14/science/14wheeler.html |archive-date=22 November 2016}}</ref>

However, the term was used by others around that time. Science writer Marcia Bartusiak traces the term "black hole" to physicist [[Robert H. Dicke]], who in the early 1960s reportedly compared the phenomenon to the [[Black Hole of Calcutta]], notorious as a prison where people entered but never left alive.
The term ''black hole'' was used in print by ''[[Life (magazine)|Life]]'' and ''[[Science News]]'' magazines in 1963, and by science journalist Ann Ewing in her article {{" '}}Black Holes' in Space", dated 18 January 1964, which was a report on a meeting of the [[American Association for the Advancement of Science]] held in Cleveland, Ohio.<ref name="Bartusiak">{{cite book |last=Bartusiak |first=Marcia |author-link=Marcia Bartusiak |title=Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled On by Hawking Became Loved |date=2015 |publisher=[[Yale University Press]] |isbn=978-0-300-21363-8 |location=New Haven, CT}}</ref>

== Properties and structure ==
A black hole is generally defined as a region of spacetime for which no [[Randomness#In the physical sciences|information-carrying]] signals or objects can escape.<ref name="fz11">{{Cite book |title=Introduction to Black Hole Physics |last1=Frolov |first1=Valeri P. |date=1 December 2011 |publisher=Oxford University Press |isbn=978-0-19-969229-3 |edition=1st |page=1 |last2=Zelnikov |first2=Andrei}}</ref><ref name="booth05">{{Cite journal |last1=Booth |first1=Ivan |title=Black-hole boundaries |journal=Canadian Journal of Physics |date=2005 |volume=83 |issue=11 |pages=1073–1099 |doi=10.1139/p05-063 |arxiv=gr-qc/0508107 |bibcode=2005CaJPh..83.1073B }}</ref> However, physicists do not have a precisely-agreed-upon definition of a black hole.<ref name="curiel19">{{Cite journal |last1=Curiel |first1=Erik |title=The many definitions of a black hole |journal=Nature Astronomy |date=2019 |volume=3 |pages=27–34 |doi=10.1038/s41550-018-0602-1 |arxiv=1808.01507 |bibcode=2019NatAs...3...27C }}</ref> From a local perspective, a black hole can be viewed as a region with a [[gravitational pull]], or, equivalently, [[spacetime curvature]] so intense that nothing can escape.<ref name="booth05" /><ref name="hamiltonwaterfall">{{Cite web |title=A Black Hole is a Waterfall of Space |url=https://jila.colorado.edu/~ajsh/insidebh/waterfall.html |last=Hamilton |first=Andrew |url-status=live |archive-url=https://web.archive.org/web/20250820063124/https://jila.colorado.edu/%7Eajsh/insidebh/waterfall.html |archive-date=20 August 2025 |access-date=24 October 2025 |website=Inside Black Holes}}</ref> A black hole may also be defined as a region where the [[escape velocity]] is greater than the speed of light, or where space is falling inwards faster than the speed of light.<ref name="bhwar">{{cite book |last=Susskind |first=Leonard |author-link=Leonard Susskind |title=The black hole war: my battle with Stephen Hawking to make the world safe for quantum mechanics |title-link=The Black Hole War |date=2008 |publisher=Little, Brown |isbn=978-0-316-01640-7 |edition=1st |location=New York |oclc=181603165}}</ref>{{rp|27}}<ref name="waterfall" /> The formula for escape velocity is <math> V = \sqrt{2MG/R}</math>, where <em>M</em> represents mass, <em>G</em> is the gravitational constant, and <em>R</em> is the radius from the center of the mass.<ref name="bhwar" /> From a global perspective, a black hole can be understood as a region of the [[universe]] for which no [[causality|causal influences]] can reach the outside.<ref name="curiel19" /><ref name="fz11" />

The [[no-hair theorem]] postulates that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, electric charge, and angular momentum; the black hole is otherwise featureless. If the conjecture is true, any two black holes that share the same values for these properties, or parameters, are indistinguishable from one another. The degree to which the conjecture is true for real black holes is currently an unsolved problem.<ref name="HeuslerNoHair">{{cite journal |vauthors=Chruściel PT, Costa JL, Heusler M |date=2012 |title=Stationary Black Holes: Uniqueness and Beyond |journal=[[Living Reviews in Relativity]] |type=Article |volume=15 |issue=7 |arxiv=1205.6112 |bibcode=2012LRR....15....7C |doi=10.12942/lrr-2012-7 |pmc=5255892 |pmid=28179837 |doi-access=free |article-number=7}}</ref>

These properties are unique because they are visible from outside a black hole. For example, a charged black hole [[Coulomb's law|repels]] other like charges just like any other charged object.<ref>{{Cite journal |last1=Xu |first1=Hao |last2=Ong |first2=Yen Chin |last3=Yung |first3=Man-Hong |title=Cosmic censorship and the evolution of <math>d</math> -dimensional charged evaporating black holes |journal=Physical Review D |date=2020 |volume=101 |issue=6 |article-number=064015 |doi=10.1103/PhysRevD.101.064015 |arxiv=1911.11990 |bibcode=2020PhRvD.101f4015X }}</ref> Similarly, the total mass of a black hole can be estimated by analyzing the motion of objects near the black hole, such as stars or gas.<ref name="peterson14"/> A black hole's angular momentum (or spin) can be measured from far away by analyzing the [[electromagnetic spectrum]] of the accretion disk—The faster the black hole is spinning, the closer matter can get to the event horizon without falling in, and the redder that matter appears due to gravitational redshift.<ref name="reynolds19">{{Cite journal|last=Reynolds|first=Christopher S.|date=January 2019|title=Observing black holes spin|url=https://www.nature.com/articles/s41550-018-0665-z|journal=Nature Astronomy|volume=3|issue=1|pages=41–47|doi=10.1038/s41550-018-0665-z|issn=2397-3366|arxiv=1903.11704|bibcode=2019NatAs...3...41R|s2cid=85543351|access-date=21 August 2020|archive-date=18 November 2020|archive-url=https://web.archive.org/web/20201118092121/https://www.nature.com/articles/s41550-018-0665-z|url-status=live}}</ref><ref>{{Cite journal |last1=Steiner |first1=James F. |last2=McClintock |first2=Jeffrey E. |last3=Remillard |first3=Ronald A. |last4=Gou |first4=Lijun |last5=Yamada |first5=Shin'ya |last6=Narayan |first6=Ramesh |title=The Constant Inner-Disk Radius of LMC X-3: A Basis for Measuring Black Hole Spin |journal=The Astrophysical Journal |date=2010 |volume=718 |issue=2 |pages=L117–L121 |doi=10.1088/2041-8205/718/2/L117 |arxiv=1006.5729 |bibcode=2010ApJ...718L.117S }}</ref> Properties of black holes can also be detected from the gravitational waves they emit.<ref name="reynolds19" /><ref>{{Cite journal |last1=Chatziioannou |first1=Katerina |last2=Lovelace |first2=Geoffrey |last3=Boyle |first3=Michael |last4=Giesler |first4=Matthew |last5=Hemberger |first5=Daniel A. |last6=Katebi |first6=Reza |last7=Kidder |first7=Lawrence E. |last8=Pfeiffer |first8=Harald P. |last9=Scheel |first9=Mark A. |last10=Szilágyi |first10=Béla |title=Measuring the properties of nearly extremal black holes with gravitational waves |journal=Physical Review D |date=2018 |volume=98 |issue=4 |article-number=044028 |doi=10.1103/PhysRevD.98.044028 |arxiv=1804.03704 |bibcode=2018PhRvD..98d4028C }}</ref><ref>{{Cite journal |last1=Poisson |first1=Eric |title=Measuring black-hole parameters and testing general relativity using gravitational-wave data from space-based interferometers |journal=Physical Review D |date=1996 |volume=54 |issue=10 |pages=5939–5953 |doi=10.1103/PhysRevD.54.5939 |pmid=10020601 |arxiv=gr-qc/9606024 |bibcode=1996PhRvD..54.5939P }}</ref><ref>{{Cite journal |last1=Echeverria |first1=Fernando |title=Gravitational-wave measurements of the mass and angular momentum of a black hole |journal=Physical Review D |date=1989 |volume=40 |issue=10 |pages=3194–3203 |doi=10.1103/PhysRevD.40.3194 |pmid=10011687 |bibcode=1989PhRvD..40.3194E }}</ref>

[[File:Anatomy of a Black Hole.jpg|center|thumb|450x450px|An artistic depiction of a black hole and its features]]

Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in, and every quantity that cannot be measured far away from the black hole horizon is lost. Additionally, because the Hawking radiation emitted from a black hole is [[thermal radiation|thermal]], it cannot carry any information about what fell into the black hole, causing the information to seemingly vanish as the black hole radiates away. Since this seemingly violates the law of [[conservation of energy]], it has been called the [[black hole information loss paradox]].<ref name="math_ucr_edu">{{cite web |url=http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/info_loss.html |title=The Black Hole Information Loss Problem |website=Usenet Physics FAQ |last=Anderson |first=Warren G. |date=1996 |access-date=24 March 2009 |archive-url=https://web.archive.org/web/20090122223839/http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/info_loss.html |archive-date=22 January 2009}}</ref><ref name="Preskill1994">{{cite conference |last=Preskill |first=J. |author-link1=John Preskill |url=http://www.theory.caltech.edu/~preskill/talks/blackholes.pdf |title=Black holes and information: A crisis in quantum physics |date=21 October 1994 |conference=Caltech Theory Seminar |archive-url=https://web.archive.org/web/20080518054438/http://www.theory.caltech.edu/~preskill/talks/blackholes.pdf |archive-date=18 May 2008 |access-date=17 May 2009 }}</ref><ref>{{Cite journal |last1=Danielsson |first1=Ulf H. |last2=Schiffer |first2=Marcelo |title=Quantum mechanics, common sense, and the black hole information paradox |journal=Physical Review D |date=1993 |volume=48 |issue=10 |pages=4779–4784 |doi=10.1103/PhysRevD.48.4779 |pmid=10016132 |arxiv=gr-qc/9305012 |bibcode=1993PhRvD..48.4779D }}</ref>

=== Physical parameters ===
[[File:Black Hole Shadow.gif|thumb|350x350px|Radii for shadow and photon sphere relative to event horizon]]

The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after [[Karl Schwarzschild]], who discovered the [[Solutions of the Einstein field equations|solution]] in 1916.<ref name="Schwarzschild1916" /> According to [[Birkhoff's theorem (relativity)|Birkhoff's theorem]], it is the only [[Vacuum solution (general relativity)|vacuum solution]] that is [[Spherically symmetric spacetime|spherically symmetric]].<ref>{{harvnb|Hawking|Ellis|1973|loc=Appendix B}}</ref> This means there is no observable difference at a distance between the gravitational field of such a black hole and that of any other spherical object of the same mass. Contrary to the popular notion of a black hole "sucking in everything" in its surroundings, from far away, the external gravitational field of a black hole is identical to that of any other body of the same mass.<ref>{{cite book |first1=Michael A. |last1=Seeds |first2=Dana E. |last2=Backman |title=Perspectives on Astronomy |page=167 |publisher=Cengage Learning |date=2007 |isbn=978-0-495-11352-2 |url=https://books.google.com/books?id=CXom04KGIL8C&pg=PA167|url-status=live |archive-url=https://web.archive.org/web/20160810211808/https://books.google.com/books?id=CXom04KGIL8C&pg=PA167 |archive-date=10 August 2016}}</ref>

Solutions describing more general black holes also exist. Non-rotating [[charged black hole]]s are described by the [[Reissner–Nordström metric]], while the Kerr metric describes a non-charged [[rotating black hole]]. The most general [[stationary spacetime|stationary]] black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum.<ref name=shapiro_teukolsky1983>{{cite book |last1=Shapiro |first1=S. L. |last2=Teukolsky |first2=S. A. |author2-link=Saul Teukolsky |title=Black holes, white dwarfs, and neutron stars: the physics of compact objects |page=357 |publisher=John Wiley and Sons |date=1983 |isbn=978-0-471-87316-7}}</ref>

While the mass of a black hole can theoretically take any positive value, the charge and angular momentum are constrained by the mass. The total electric charge&nbsp;''Q'' and the total angular momentum&nbsp;''J'' are expected to satisfy the inequality
<math display="block">\frac{Q^2}{4\pi\epsilon_0} + \frac{c^2 J^2}{G M^2} \le G M^2</math>
for a black hole of mass ''M''. Black holes with the minimum possible mass satisfying this inequality are called [[extremal black hole|extremal]]. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have so-called [[naked singularity|naked singularities]] that can be observed from the outside.<ref name="wald 1997">{{cite book |last=Wald |first=R. M. |author-link=Robert Wald |title=Black Holes, Gravitational Radiation and the Universe |editor1=Iyer, B. R. |editor2=Bhawal, B. |chapter=Gravitational Collapse and Cosmic Censorship |arxiv=gr-qc/9710068 |date=1997 |pages=69–86 |location=Dordrecht |publisher=Springer |doi=10.1007/978-94-017-0934-7 |isbn=978-94-017-0934-7}}</ref> Because these singularities make the universe inherently unpredictable, many physicists believe they could not exist.<ref>{{cite journal |last=Berger |first=B. K.|author-link= Beverly Berger |date=2002 |title=Numerical Approaches to Spacetime Singularities |journal=Living Reviews in Relativity |volume=5 |issue=1 |pages=2002–1|article-number=1 |bibcode=2002LRR.....5....1B |doi=10.12942/lrr-2002-1 |doi-access=free |pmid=28179859 |pmc=5256073 |arxiv=gr-qc/0201056}}</ref> The [[weak cosmic censorship hypothesis]], proposed by [[Sir Roger Penrose]], rules out the formation of such singularities, when they are created through the gravitational collapse of [[energy conditions|realistic matter]]. However, this theory has not yet been proven, and some physicists believe that naked singularities could exist.<ref name="joshi09">{{Cite magazine |date=1 February 2009 |title=Naked Singularities |magazine=[[Scientific American]] |last=Joshi |first=Pankaj S.  |pages=36–43 |volume=300 |issue=2 |jstor=26001219 }}</ref> It is also unknown whether black holes could even become extremal, forming naked singularities, since natural processes counteract increasing spin and charge when a black hole becomes near-extremal.<ref name="joshi09" /><ref>{{Cite journal |last1=Reynolds |first1=Christopher S. |title=The spin of supermassive black holes |journal=Classical and Quantum Gravity |date=2013 |volume=30 |issue=24 |doi=10.1088/0264-9381/30/24/244004 |arxiv=1307.3246 |bibcode=2013CQGra..30x4004R }}</ref><ref>{{Cite journal |last1=Ghosh |first1=Rajes |last2=Mishra |first2=Akash K. |last3=Sarkar |first3=Sudipta |title=Overcharging extremal black holes |journal=Physical Review D |date=2021 |volume=104 |issue=10 |article-number=104043 |doi=10.1103/PhysRevD.104.104043 |arxiv=2106.10667 |bibcode=2021PhRvD.104j4043G }}</ref>

==== Charge ====
Most black holes are believed to have an approximately neutral charge. For example, Michal Zajaček, Arman Tursunov, Andreas Eckart, and Silke Britzen found the [[electric charge]] of Sagittarius A*, the black hole at the center of the Milky Way galaxy, to be at least ten orders of magnitude below the theoretical maximum.<ref name="zteb18" /> If a black hole were to become charged, particles with an opposite sign of charge would be pulled in by the extra [[electromagnetism|electromagnetic force]], while particles with the same sign of charge would be repelled, neutralizing the black hole. This effect may not be as strong if the black hole is also spinning.<ref>{{Cite journal |last1=Gong |first1=Yi |last2=Cao |first2=Zhoujian |last3=Gao |first3=He |last4=Zhang |first4=Bing |title=On neutralization of charged black holes |journal=Monthly Notices of the Royal Astronomical Society |date=2019 |volume=488 |issue=2 |pages=2722–2731 |doi=10.1093/mnras/stz1904 |doi-access=free |arxiv=1907.05239 }}</ref> The presence of charge can reduce the diameter of the black hole by up to 38% and moves the innermost stable circular orbit inwards, regardless whether the particles in the ISCO are [[electrically charged]] or electrically neutral.<ref name="zteb18">{{Cite journal |last1=Zajaček |first1=Michal |last2=Tursunov |first2=Arman |last3=Eckart |first3=Andreas |last4=Britzen |first4=Silke |title=On the charge of the Galactic centre black hole |journal=Monthly Notices of the Royal Astronomical Society |date=2018 |volume=480 |issue=4 |pages=4408–4423 |doi=10.1093/mnras/sty2182 |doi-access=free |arxiv=1808.07327 }}</ref><ref>{{Cite journal |last1=Zakharov |first1=A. F. |last2=De Paolis |first2=F. |last3=Ingrosso |first3=G. |last4=Nucita |first4=A. A. |title=Direct measurements of black hole charge with future astrometrical missions |journal=Astronomy & Astrophysics |date=2005 |volume=442 |issue=3 |pages=795–799 |doi=10.1051/0004-6361:20053432 |arxiv=astro-ph/0505286 |bibcode=2005A&A...442..795Z }}</ref>

The charge Q for a nonspinning black hole is bounded by
<math display="block">Q\leq\sqrt{G}M,</math>
where G is the gravitational constant and M is the black hole's mass.<ref>{{Cite journal |last1=Turimov |first1=Bobur |last2=Boboqambarova |first2=Madina |last3=Ahmedov |first3=Bobomurat |last4=Stuchlík |first4=Zdeněk |title=Distinguishable feature of electric and magnetic charged black hole |journal=The European Physical Journal Plus |date=2022 |volume=137 |issue=2 |article-number=222 |doi=10.1140/epjp/s13360-022-02390-7}}</ref>

==== Spin ====
Unlike charge, rotation is expected to be a universal feature of compact astrophysical objects, with many black holes spinning at near the maximum rate.<ref>{{Cite web |title=Black Hole Basics |url=https://science.nasa.gov/universe/black-holes/ |access-date=25 October 2025 |website=NASA.gov |date=13 March 2024 }}</ref><ref name="daly19">{{Cite journal |last1=Daly |first1=Ruth A. |title=Black Hole Spin and Accretion Disk Magnetic Field Strength Estimates for More Than 750 Active Galactic Nuclei and Multiple Galactic Black Holes |journal=The Astrophysical Journal |date=2019 |volume=886 |issue=1 |page=37 |doi=10.3847/1538-4357/ab35e6 |arxiv=1905.11319 |bibcode=2019ApJ...886...37D |doi-access=free }}</ref><ref name="eo16">{{Cite journal |last1=Eilon |first1=Ehud |last2=Ori |first2=Amos |title=Numerical study of the gravitational shock wave inside a spherical charged black hole |journal=Physical Review D |date=2016 |volume=94 |issue=10 |article-number=104060 |doi=10.1103/PhysRevD.94.104060 |arxiv=1610.04355 |bibcode=2016PhRvD..94j4060E }}</ref> For example, the Milky Way's central black hole Sagittarius A* rotates at about 90% of the maximum rate.<ref name="daly19" /><ref>{{Cite journal |last1=Daly |first1=Ruth A. |last2=Donahue |first2=Megan |last3=o'Dea |first3=Christopher P. |last4=Sebastian |first4=Biny |last5=Haggard |first5=Daryl |last6=Lu |first6=Anan |title=New black hole spin values for Sagittarius A* obtained with the outflow method |journal=Monthly Notices of the Royal Astronomical Society |date=2024 |volume=527 |pages=428–436 |doi=10.1093/mnras/stad3228 |doi-access=free }}</ref> The supermassive black hole in the center of the [[Messier 87|M87 galaxy]] appears to have an angular momentum very close to the maximum allowed value.<ref name="daly19" /><ref>{{Cite journal |last1=Tamburini |first1=Fabrizio |last2=Thidé |first2=Bo |last3=Della Valle |first3=Massimo |title=Measurement of the spin of the M87 black hole from its observed twisted light |journal=Monthly Notices of the Royal Astronomical Society: Letters |date=2020 |volume=492 |pages=L22–L27 |doi=10.1093/mnrasl/slz176 |doi-access=free |arxiv=1904.07923 }}</ref><ref>{{Cite journal |last1=Bambi |first1=Cosimo |last2=Freese |first2=Katherine |last3=Vagnozzi |first3=Sunny |last4=Visinelli |first4=Luca |title=Testing the rotational nature of the supermassive object M87* from the circularity and size of its first image |journal=Physical Review D |date=2019 |volume=100 |issue=4 |article-number=044057 |doi=10.1103/PhysRevD.100.044057 |arxiv=1904.12983 |bibcode=2019PhRvD.100d4057B }}</ref> That uncharged limit is<ref name="50SMBH" />
<math display="block">J \le \frac{GM^{2}}{c},</math>
allowing definition of a [[dimensionless]] spin parameter such that<ref name="50SMBH" />
<math display="block"> 0 \le \frac{cJ}{GM^{2}}\le 1.</math><ref name="50SMBH">{{cite journal |doi=10.1103/PhysRevLett.118.221101 |pmid=28621973 |title=GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2 |journal=[[Physical Review Letters]] |date=1 June 2017 |first=B. P. |last=Abbott |collaboration=[[LIGO Scientific Collaboration]] and Virgo Collaboration |volume=118 |issue=22 |article-number=221101 |arxiv=1706.01812 |bibcode=2017PhRvL.118v1101A|s2cid=206291714 }}</ref>{{refn|group=Note|The value of ''cJ/GM{{sup|2}}'' can exceed{{nbsp}}1 for objects other than black holes. The largest value known for a neutron star is ≤ 0.4, and commonly used equations of state would limit that value to < 0.7.<ref name="PRL-171016">{{cite journal |last1=Abbott |first1=B. P. |display-authors=et al |collaboration=[[LIGO Scientific Collaboration]] & [[Virgo interferometer|Virgo Collaboration]] |title=GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral |journal=Physical Review Letters |date=16 October 2017 |volume=119 |issue=16 |article-number=161101 |doi=10.1103/PhysRevLett.119.161101 |pmid=29099225 |arxiv=1710.05832 |bibcode=2017PhRvL.119p1101A|s2cid=217163611 }}</ref>}}

{|class="wikitable" style="float:right; margin:0 0 0.5em 1em;"
|+ Black hole classifications
|-
! Class !! Approx.<br />mass !! Approx.<br />radius
|-
|[[Supermassive black hole#Ultramassive black holes|Ultramassive black hole]] ||style="text-align: center;"| {{10^|9}}–{{solar mass|{{10^|11}}}}  ||style="text-align: center;"|>1,000 [[Astronomical unit|AU]]
|-
|[[Supermassive black hole]] ||style="text-align: center;"| {{10^|6}}–{{solar mass|{{10^|9}}}} ||style="text-align: center;"|0.001–400 [[Astronomical unit|AU]]
|-
|[[Intermediate-mass black hole]] ||style="text-align: center;"| {{10^|2}}–{{solar mass|{{10^|5}}}} ||style="text-align: center;"|10{{sup|3}} km ≈ [[Earth radius|''R''{{sub|Earth}}]]
|-
|[[Stellar black hole]] ||style="text-align: center;"| {{solar mass|2–150}} ||style="text-align: center;"|30&nbsp;km
|-
|[[Micro black hole]] ||style="text-align: center;"|up to ''M''{{sub|[[Moon]]}} ||style="text-align: center;"|up to 0.1&nbsp;mm
|}

==== Mass ====
Black holes can have a wide range of masses. The minimum mass of a black hole formed by stellar gravitational collapse is governed by the maximum mass of a neutron star and is believed to be approximately two-to-four solar masses.<ref>{{Cite journal |last1=Cromartie |first1=H. T. |last2=Fonseca |first2=E. |last3=Ransom |first3=S. M. |last4=Demorest |first4=P. B. |last5=Arzoumanian |first5=Z. |last6=Blumer |first6=H. |last7=Brook |first7=P. R. |last8=Decesar |first8=M. E. |last9=Dolch |first9=T. |last10=Ellis |first10=J. A. |last11=Ferdman |first11=R. D. |last12=Ferrara |first12=E. C. |last13=Garver-Daniels |first13=N. |last14=Gentile |first14=P. A. |last15=Jones |first15=M. L. |last16=Lam |first16=M. T. |last17=Lorimer |first17=D. R. |last18=Lynch |first18=R. S. |last19=McLaughlin |first19=M. A. |last20=Ng |first20=C. |last21=Nice |first21=D. J. |last22=Pennucci |first22=T. T. |last23=Spiewak |first23=R. |last24=Stairs |first24=I. H. |last25=Stovall |first25=K. |last26=Swiggum |first26=J. K. |last27=Zhu |first27=W. W. |title=Relativistic Shapiro delay measurements of an extremely massive millisecond pulsar |journal=Nature Astronomy |date=2019 |volume=4 |pages=72–76 |doi=10.1038/s41550-019-0880-2 |arxiv=1904.06759 }}</ref><ref>{{Cite journal |last1=Drischler |first1=Christian |last2=Han |first2=Sophia |last3=Lattimer |first3=James M. |last4=Prakash |first4=Madappa |last5=Reddy |first5=Sanjay |last6=Zhao |first6=Tianqi |title=Limiting masses and radii of neutron stars and their implications |journal=Physical Review C |date=2021 |volume=103 |issue=4 |article-number=045808 |doi=10.1103/PhysRevC.103.045808 |arxiv=2009.06441 |bibcode=2021PhRvC.103d5808D }}</ref><ref>{{Cite journal |last1=Farr |first1=Will M. |last2=Sravan |first2=Niharika |last3=Cantrell |first3=Andrew |last4=Kreidberg |first4=Laura |last5=Bailyn |first5=Charles D. |last6=Mandel |first6=Ilya |last7=Kalogera |first7=Vicky |title=The Mass Distribution of Stellar-Mass Black Holes |journal=The Astrophysical Journal |date=2011 |volume=741 |issue=2 |page=103 |doi=10.1088/0004-637X/741/2/103 |arxiv=1011.1459 |bibcode=2011ApJ...741..103F }}</ref> However, theoretical [[primordial black hole]]s, believed to have formed soon after the Big Bang, could be far smaller, with masses as little as {{val|e=-5|u=grams}} at formation.<ref>{{Cite journal |last1=Carr |first1=Bernard |last2=Kohri |first2=Kazunori |last3=Sendouda |first3=Yuuiti |last4=Yokoyama |first4=Jun'Ichi |title=Constraints on primordial black holes |journal=Reports on Progress in Physics |date=2021 |volume=84 |issue=11 |doi=10.1088/1361-6633/ac1e31 |pmid=34874316 |arxiv=2002.12778 |bibcode=2021RPPh...84k6902C }}</ref> These very small black holes are sometimes called [[micro black hole]]s.<ref>{{Cite journal |last1=Nakama |first1=Tomohiro |last2=Yokoyama |first2=Jun'Ichi |title=Micro black holes formed in the early Universe and their cosmological implications |journal=Physical Review D |date=2019 |volume=99 |issue=6 |article-number=061303 |doi=10.1103/PhysRevD.99.061303 |arxiv=1811.05049 |bibcode=2019PhRvD..99f1303N }}</ref><ref>{{Cite journal |last1=Scardigli |first1=Fabio |title=Gravity coupling from micro-black holes |journal=Nuclear Physics B - Proceedings Supplements |date=2000 |volume=88 |issue=1–3 |pages=291–294 |doi=10.1016/S0920-5632(00)00788-X |arxiv=hep-th/9907150 |bibcode=2000NuPhS..88..291S }}</ref>

Black holes formed by stellar collapse are called stellar black holes. Estimates of their maximum mass at formation vary, but generally range from 10 to 100 solar masses, with higher estimates for black holes progenated by [[metallicity|low-metallicity]] stars.<ref>{{Cite journal |last1=Belczynski |first1=Krzysztof |last2=Bulik |first2=Tomasz |last3=Fryer |first3=Chris L. |last4=Ruiter |first4=Ashley |last5=Valsecchi |first5=Francesca |last6=Vink |first6=Jorick S. |last7=Hurley |first7=Jarrod R. |title=On the Maximum Mass of Stellar Black Holes |journal=The Astrophysical Journal |date=2010 |volume=714 |issue=2 |pages=1217–1226 |doi=10.1088/0004-637X/714/2/1217 |arxiv=0904.2784 |bibcode=2010ApJ...714.1217B }}</ref><ref>{{Cite journal |last1=Fryer |first1=Chris L. |last2=Kalogera |first2=Vassiliki |title=Theoretical Black Hole Mass Distributions |journal=The Astrophysical Journal |date=2001 |volume=554 |issue=1 |pages=548–560 |doi=10.1086/321359 |arxiv=astro-ph/9911312 |bibcode=2001ApJ...554..548F }}</ref><ref>{{Cite journal |last1=Fryer |first1=Chris L. |title=Mass Limits for Black Hole Formation |journal=The Astrophysical Journal |date=1999 |volume=522 |issue=1 |pages=413–418 |doi=10.1086/307647 |arxiv=astro-ph/9902315 |bibcode=1999ApJ...522..413F }}</ref><ref>{{Cite journal |last1=Vink |first1=Jorick S. |last2=Higgins |first2=Erin R. |last3=Sander |first3=Andreas A C. |last4=Sabhahit |first4=Gautham N. |title=Maximum black hole mass across cosmic time |journal=Monthly Notices of the Royal Astronomical Society |date=2021 |volume=504 |pages=146–154 |doi=10.1093/mnras/stab842 |doi-access=free |arxiv=2010.11730 }}</ref><ref name="mc04">{{Cite journal |last1=Coleman Miller |first1=M. |last2=Colbert |first2=E. J. M. |title=Intermediate-Mass Black Holes |journal=International Journal of Modern Physics D |date=2004 |volume=13 |issue=1 |pages=1–64 |doi=10.1142/S0218271804004426 |arxiv=astro-ph/0308402 |bibcode=2004IJMPD..13....1M }}</ref> These black holes can also gain mass via accretion of nearby matter.<ref>{{Cite journal |last1=Lupi |first1=A. |last2=Haardt |first2=F. |last3=Dotti |first3=M. |last4=Fiacconi |first4=D. |last5=Mayer |first5=L. |last6=Madau |first6=P. |title=Growing massive black holes through supercritical accretion of stellar-mass seeds |journal=Monthly Notices of the Royal Astronomical Society |date=2016 |volume=456 |issue=3 |pages=2993–3003 |doi=10.1093/mnras/stv2877 |doi-access=free |arxiv=1512.02651 }}</ref> Stellar black holes are often found in [[x-ray binary|binaries]] with stars.<ref name="lph97">{{Cite journal |last1=Dunn |first1=R. J. H. |last2=Fender |first2=R. P. |last3=Körding |first3=E. G. |last4=Belloni |first4=T. |last5=Cabanac |first5=C. |title=A global spectral study of black hole X-ray binaries |journal=Monthly Notices of the Royal Astronomical Society |date=2010 |volume=403 |issue=1 |pages=61–82 |doi=10.1111/j.1365-2966.2010.16114.x |arxiv=0912.0142 |bibcode=2010MNRAS.403...61D |doi-access=free }}</ref><ref>{{Cite book |title=X-ray Binaries |date=28 January 1997 |publisher=Cambridge University Press |isbn=978-0-521-59934-4 |page=1 |editor-last=Lewin |editor-first=Walter H. G. |editor-last2=Jan |editor-first2=van Paradijs |editor-last3=van den Heuvel |editor-first3=Edward P.J.}}</ref><ref>{{Cite journal|last1=Shao |first1=Yong |last2=Li |first2=Xiang-Dong |title=Population Synthesis of Black Hole X-Ray Binaries |journal=The Astrophysical Journal |date=2020 |volume=898 |issue=2 |page=143 |doi=10.3847/1538-4357/aba118 |arxiv=2006.15961 |bibcode=2020ApJ...898..143S |doi-access=free }}</ref> These binaries can be categorized as either <em>low-mass</em> or <em>high-mass</em>; This classification is based on the mass of the companion star, not the compact object itself.<ref name="lph97" /> Stellar black holes are also sometimes found in binaries with other compact objects, such as [[white dwarf]]s,<ref name="lph97" /> neutron stars,<ref>{{Cite journal |last1=Broekgaarden |first1=Floor S. |last2=Berger |first2=Edo |title=Formation of the First Two Black Hole–Neutron Star Mergers (GW200115 and GW200105) from Isolated Binary Evolution |journal=The Astrophysical Journal Letters |date=2021 |volume=920 |issue=1 |pages=L13 |doi=10.3847/2041-8213/ac2832 |arxiv=2108.05763 |bibcode=2021ApJ...920L..13B |doi-access=free }}</ref><ref>{{Cite journal |last1=Chattopadhyay |first1=Debatri |last2=Stevenson |first2=Simon |last3=Broekgaarden |first3=Floor |last4=Antonini |first4=Fabio |last5=Belczynski |first5=Krzysztof |title=Modelling the formation of the first two neutron star–black hole mergers, GW200105 and GW200115: Metallicity, chirp masses, and merger remnant spins |journal=Monthly Notices of the Royal Astronomical Society |date=2022 |volume=513 |issue=4 |pages=5780–5789 |doi=10.1093/mnras/stac1283 |doi-access=free }}</ref> and other black holes.<ref>{{Cite journal |last1=Ziosi |first1=B. M. |last2=Mapelli |first2=M. |last3=Branchesi |first3=M. |last4=Tormen |first4=G. |title=Dynamics of stellar black holes in young star clusters with different metallicities - II. Black hole-black hole binaries |journal=Monthly Notices of the Royal Astronomical Society |date=2014 |volume=441 |issue=4 |pages=3703–3717 |doi=10.1093/mnras/stu824 |doi-access=free |arxiv=1404.7147 }}</ref><ref>{{Cite web |title=Sources and Types of Gravitational Waves |url=https://www.ligo.caltech.edu/page/gw-sources |access-date=26 October 2025 |website=LIGO Caltech}}</ref>

Black holes that are larger than stellar black holes but smaller than supermassive black holes are called [[intermediate-mass black hole]]s, with masses of approximately {{value|e=2}} to {{value|e=5}} solar masses. These black holes seem to be rarer than their stellar and supermassive counterparts, with relatively few candidates having been observed.<ref name="nasa20">{{Cite web |title=Black Hole Types |url=https://science.nasa.gov/universe/black-holes/types |access-date=26 October 2025 |website=NASA.gov |date=21 October 2020 }}</ref><ref name="mc04"/><ref>{{Cite journal |last1=Caputo |first1=Daniel P. |last2=De Vries |first2=Nathan |last3=Patruno |first3=Alessandro |last4=Portegies Zwart |first4=Simon |title=On Estimating the Total Number of Intermediate Mass Black Holes |journal=Monthly Notices of the Royal Astronomical Society |date=2017 |article-number=stw3336 |doi=10.1093/mnras/stw3336 |doi-access=free }}</ref> Physicists have speculated that such black holes may form from collisions in [[globular cluster|globular]] and [[star cluster|star]] clusters or at the center of [[dwarf galaxy|low-mass galaxies]].<ref>{{Cite journal |last1=Coleman Miller |first1=M. |last2=Hamilton |first2=Douglas P. |title=Production of intermediate-mass black holes in globular clusters |journal=Monthly Notices of the Royal Astronomical Society |date=2002 |volume=330 |issue=1 |pages=232–240 |doi=10.1046/j.1365-8711.2002.05112.x |arxiv=astro-ph/0106188 |bibcode=2002MNRAS.330..232C |doi-access=free }}</ref><ref>{{Cite journal |last1=Rizzuto |first1=Francesco Paolo |last2=Naab |first2=Thorsten |last3=Spurzem |first3=Rainer |last4=Giersz |first4=Mirek |last5=Ostriker |first5=J. 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C. |last7=Wang |first7=Long |last8=Berczik |first8=Peter |last9=Rampp |first9=M. |title=Intermediate mass black hole formation in compact young massive star clusters |journal=Monthly Notices of the Royal Astronomical Society |date=2021 |volume=501 |issue=4 |pages=5257–5273 |doi=10.1093/mnras/staa3634 |doi-access=free |arxiv=2008.09571 }}</ref><ref>{{Cite journal |last1=Fujii |first1=Michiko S. |last2=Wang |first2=Long |last3=Tanikawa |first3=Ataru |last4=Hirai |first4=Yutaka |last5=Saitoh |first5=Takayuki R. |title=Simulations predict intermediate-mass black hole formation in globular clusters |journal=Science |date=2024 |volume=384 |issue=6703 |pages=1488–1492 |doi=10.1126/science.adi4211 |pmid=38815090 |arxiv=2406.06772 |bibcode=2024Sci...384.1488F }}</ref><ref>{{Cite journal |last1=Barai |first1=Paramita |last2=De Gouveia Dal Pino |first2=Elisabete M. |title=Intermediate-mass black hole growth and feedback in dwarf galaxies at high redshifts |journal=Monthly Notices of the Royal Astronomical Society |date=2019 |volume=487 |issue=4 |pages=5549–5563 |doi=10.1093/mnras/stz1616 |doi-access=free |arxiv=1807.04768 }}</ref><ref>{{Cite journal |last1=Beckmann |first1=R. S. |last2=Dubois |first2=Y. |last3=Volonteri |first3=M. |last4=Dong-Páez |first4=C. A. |last5=Trebitsch |first5=M. |last6=Devriendt |first6=J. |last7=Kaviraj |first7=S. |last8=Kimm |first8=T. |last9=Peirani |first9=S. |title=Population statistics of intermediate-mass black holes in dwarf galaxies using the newhorizon simulation |journal=Monthly Notices of the Royal Astronomical Society |date=2023 |volume=523 |issue=4 |pages=5610–5623 |doi=10.1093/mnras/stad1544 |doi-access=free |arxiv=2211.13301 }}</ref> They may also form as the result of mergers of smaller black holes, with several LIGO observations finding merged black holes within the 110-350 solar mass range.<ref>{{Cite journal |last1=Ruiz-Rocha |first1=Krystal |last2=Yelikar |first2=Anjali B. |last3=Lange |first3=Jacob |last4=Gabella |first4=William |last5=Weller |first5=Robert A. |last6=o'Shaughnessy |first6=Richard |last7=Holley-Bockelmann |first7=Kelly |last8=Jani |first8=Karan |title=Properties of "Lite" Intermediate-mass Black Hole Candidates in LIGO-Virgo's Third Observing Run |journal=The Astrophysical Journal Letters |date=2025 |volume=985 |issue=2 |pages=L37 |doi=10.3847/2041-8213/adc5f8 |arxiv=2502.17681 |bibcode=2025ApJ...985L..37R |doi-access=free }}</ref><ref>{{Cite journal |last1=Abbott |first1=R. |last2=Abbott |first2=T. 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The black holes with the largest masses are called [[supermassive black hole]]s, with masses more than {{value|e=6}} times that of the Sun.<ref name="nasa20" /><ref>{{Cite web |title=Black Holes |url=https://www.cfa.harvard.edu/research/topic/black-holes |access-date=26 October 2025 |website=Center for Astrophysics}}</ref><ref>{{Cite book |last1=Mezcua |first1=Mar |title=Encyclopedia of Astrobiology |chapter=Black Holes |date=2021 |pages=1–8 |doi=10.1007/978-3-642-27833-4_5510-1 |arxiv=2110.08629 |isbn=978-3-642-27833-4 }}</ref> These black holes are believed to exist at the centers of almost every large galaxy, including the Milky Way.<ref name="ff05" /><ref name="peterson14" /><ref>{{Cite journal |last1=Broderick |first1=Avery E. |last2=Loeb |first2=Abraham |last3=Narayan |first3=Ramesh |title=The Event Horizon of Sagittarius A |journal=The Astrophysical Journal |date=2009 |volume=701 |issue=2 |pages=1357–1366 |doi=10.1088/0004-637X/701/2/1357 |arxiv=0903.1105 |bibcode=2009ApJ...701.1357B }}</ref><ref>{{Cite journal |last1=Yuan |first1=Feng |last2=Quataert |first2=Eliot |last3=Narayan |first3=Ramesh |title=On the Nature of the Variable Infrared Emission from Sagittarius A |journal=The Astrophysical Journal |date=2004 |volume=606 |issue=2 |pages=894–899 |doi=10.1086/383117 |arxiv=astro-ph/0401429 |bibcode=2004ApJ...606..894Y }}</ref> Scientists have speculated that these black holes formed via the collapse of large [[population III star]]s, [[direct collapse black hole|direct collapse]] of large amounts of matter, or the merging of many smaller black holes.<ref>{{Cite journal |last1=Volonteri |first1=Marta |title=Formation of supermassive black holes |journal=The Astronomy and Astrophysics Review |date=2010 |volume=18 |issue=3 |pages=279–315 |doi=10.1007/s00159-010-0029-x |arxiv=1003.4404 |bibcode=2010A&ARv..18..279V }}</ref><ref name="gaete24"/><ref name="gaete24">{{Cite journal |last1=Choi |first1=Jun-Hwan |last2=Shlosman |first2=Isaac |last3=Begelman |first3=Mitchell C. |title=Supermassive Black Hole Formation at High Redshifts Via Direct Collapse: Physical Processes in the Early Stage |journal=The Astrophysical Journal |date=2013 |volume=774 |issue=2 |page=149 |doi=10.1088/0004-637X/774/2/149 |arxiv=1304.1369 |bibcode=2013ApJ...774..149C }}</ref> Some scientists have proposed a subcategory of even larger black holes, called [[ultramassive black hole]]s, with masses greater than {{value|e=9}}-{{value|e=10}} solar masses.<ref name="gaete24" /><ref>{{Cite journal |last1=Natarajan |first1=Priyamvada |last2=Treister |first2=Ezequiel |title=Is there an upper limit to black hole masses? |journal=Monthly Notices of the Royal Astronomical Society |date=2009 |volume=393 |issue=3 |pages=838–845 |doi=10.1111/j.1365-2966.2008.13864.x |arxiv=0808.2813 |bibcode=2009MNRAS.393..838N |doi-access=free }}</ref><ref>{{Cite journal |last1=Dullo |first1=Bililign T. |last2=Gil De Paz |first2=Armando |last3=Knapen |first3=Johan H. |title=Ultramassive Black Holes in the Most Massive Galaxies: M <sub>BH</sub>–σ versus M <sub>BH</sub>–R <sub>b</sub> |journal=The Astrophysical Journal |date=2021 |volume=908 |issue=2 |page=134 |doi=10.3847/1538-4357/abceae |arxiv=2012.04471 |bibcode=2021ApJ...908..134D |doi-access=free }}</ref> It is unlikely that black holes with masses greater than 50-100 billion times that of the Sun could exist now, as black hole growth is limited by the age of the universe.<ref>{{cite journal | title=How big can a black hole grow? | last1=King | first1=Andrew | journal=Monthly Notices of the Royal Astronomical Society: Letters | volume=456 | issue=1 | pages=L109–L112 | date=February 2016 | doi=10.1093/mnrasl/slv186 | doi-access=free | bibcode=2016MNRAS.456L.109K | arxiv=1511.08502 | s2cid=40147275 }}</ref><ref>{{cite web | url=https://futurism.com/is-there-a-size-limit-to-how-large-a-black-hole-can-become | title=Is There a Limit to How Large Black Holes Can Become? | first1=Jaime | last1=Trosper | date=May 5, 2014 | website=futurism.com | access-date=November 27, 2018}}</ref><ref>{{cite web | url=https://www.science.org/content/article/limit-how-big-black-holes-can-grow-astonishing | title=Limit to how big black holes can grow is astonishing | first1=Daniel | last1=Clery | date=December 21, 2015 | website=sciencemag.org | access-date=November 27, 2018}}</ref><ref>{{cite web | url=https://www2.le.ac.uk/offices/press/press-releases/2015/december/black-holes-could-grow-as-large-as-50-billion-suns-before-their-food-crumbles-into-stars-research-shows | title=Black holes could grow as large as 50 billion suns before their food crumbles into stars, research shows | publisher=University of Leicester | access-date=November 27, 2018 | archive-date=October 25, 2021 | archive-url=https://web.archive.org/web/20211025005826/https://www2.le.ac.uk/offices/press/press-releases/2015/december/black-holes-could-grow-as-large-as-50-billion-suns-before-their-food-crumbles-into-stars-research-shows | url-status=dead }}</ref>

==== Radius ====
For a nonspinning, uncharged black hole, the radius of the event horizon, or Schwarzschild radius, is proportional to the mass, ''M'', through
<math display="block">r_\mathrm{s}=\frac{2GM}{c^2} \approx 2.95\, \frac{M}{M_\odot}~\mathrm{km,}</math>
where ''r''{{sub|s}} is the Schwarzschild radius and {{solar mass}} is the [[solar mass|mass of the Sun]].<ref>{{harvnb|Wald|1984|pp=124–125}}</ref> For a black hole with nonzero spin or electric charge, the radius is smaller,{{refn|group=Note|The (outer) event horizon radius scales as: <math>M + \sqrt{M^2 - {{(J/M)}}^2 - Q^2}.</math>}} until an extremal black hole could have an event horizon close to
<math display="block">r_\mathrm{+}=\frac{GM}{c^2},</math>
half the radius of a nonspinning, uncharged black hole of the same mass.<ref>{{cite journal |last1=Saa |first1=Alberto |last2=Santarelli |first2=Raphael |title=Destroying a near-extremal Kerr–Newman black hole |journal=Physical Review D |date=18 July 2011 |volume=84 |issue=2 |article-number=027501 |doi=10.1103/PhysRevD.84.027501 |arxiv=1105.3950 |bibcode=2011PhRvD..84b7501S|s2cid=118487989 }}</ref>

===External geometry===
==== Ergosphere ====
{{main|Ergosphere}}
[[File:Ergosphere and event horizon of a rotating black hole (no animation).gif|thumb|The ergosphere is a region outside of the event horizon, where objects cannot remain in place.<ref name=viss>{{cite arXiv |eprint=0706.0622 |last1=Visser |first1=Matt |title=The Kerr spacetime: A brief introduction |class=gr-qc |year=2007 |at=page 35, Fig. 3}}</ref>]]

General relativity predicts that any rotating mass will slightly "drag" along the spacetime immediately surrounding it. This will cause the spacetime around the mass to rotate around it, similar to a vortex. The rotating spacetime will then drag any matter and light in it into rotation around the spinning mass as well. This effect, called ''frame dragging'', gets stronger closer to the spinning mass.<ref name="reynolds18">{{Cite journal |last1=Reynolds |first1=Christopher S. |title=Observing black holes spin |journal=Nature Astronomy |date=2019 |volume=3 |pages=41–47 |doi=10.1038/s41550-018-0665-z |arxiv=1903.11704 |bibcode=2019NatAs...3...41R }}</ref>

Near a rotating black hole, this effect becomes very strong. In fact, rotating black holes are surrounded by a region of spacetime in which it is impossible to stay still, called the ergosphere. This is because frame dragging is so strong near the event horizon that an object would have to move faster than the [[speed of light]] in the opposite direction to just stay still.<ref>{{harvnb|Carroll|2004|loc=Ch. 6.6}}</ref><ref name="reynolds18" />

The ergosphere of a black hole is a volume bounded by the black hole's event horizon and the ''ergosurface'', which coincides with the event horizon at the poles but is at a much greater distance around the equator.<ref name=viss />

Matter and radiation can escape from the ergosphere. Through the [[Penrose process]], objects can emerge from the ergosphere with more energy than they entered with. The extra energy is taken from the rotational energy of the black hole, slowing down the rotation of the black hole.<ref>{{harvnb|Carroll|2004|loc=Ch. 6.7}}</ref> A variation of the Penrose process in the presence of strong magnetic fields, the [[Blandford–Znajek process]], is considered a likely mechanism for the enormous luminosity and relativistic jets of [[quasars]] and other [[active galactic nuclei]].<ref name="lwb00">{{Cite journal |last1=Lee |first1=Hyun Kyu |last2=Wijers |first2=R.A.M.J. |last3=Brown |first3=G.E. |title=The Blandford–Znajek process as a central engine for a gamma-ray burst |journal=Physics Reports |date=2000 |volume=325 |issue=3 |pages=83–114 |doi=10.1016/S0370-1573(99)00084-8 |arxiv=astro-ph/9906213 |bibcode=2000PhR...325...83L }}</ref>

====Accretion disk====
{{Main|Accretion disk}}
[[File:Black Hole Desktop & Phone Wallpapers (SVS14146 - BH accretion disk viz desktop).png|thumb|A black hole with an orange accretion disk. The parts of the disk circling over and under the hole are actually gravitationally lensed from the back side of the black hole.<ref>{{Cite web |title=Black Hole Anatomy |url=https://science.nasa.gov/universe/black-holes/anatomy/ |archive-url=https://web.archive.org/web/20250424044622/https://science.nasa.gov/universe/black-holes/anatomy/ |archive-date=24 April 2025 |access-date=13 October 2025 |website=NASA Science |date=2 August 2022 }}</ref><ref>{{Cite journal |title=Lensing and shadow of a black hole surrounded by a heavy accretion disk |journal=Journey of Cosmology and Astroparticle Physics |last1=Cunha |first1=Pedro |date=16 March 2020 |url=https://iopscience.iop.org/article/10.1088/1475-7516/2020/03/035 |volume=2020 |issue=3 |via=IOPscience |last2=Eiró |first2=Nelson |last3=Herdeiro |first3=Carlos |last4=Lemos |first4=José |page=035 |arxiv=1912.08833 |doi=10.1088/1475-7516/2020/03/035 |bibcode=2020JCAP...03..035C }}</ref>]]
Due to [[conservation of angular momentum]], gas falling into the [[gravitational well]] created by a massive object will typically form a disk-like structure around the object.<ref>{{cite news|url=https://phys.org/news/2018-02-dynamics-black-hole-rotational-energy.html|title=Researchers clarify dynamics of black hole rotational energy|access-date=17 September 2018|archive-date=17 September 2018|archive-url=https://web.archive.org/web/20180917105330/https://phys.org/news/2018-02-dynamics-black-hole-rotational-energy.html|url-status=live}}</ref> As the disk's angular momentum is transferred outward due to internal processes, its matter falls farther inward, converting its gravitational energy into heat and releasing a large [[flux]] of x-rays.<ref name=McClintockRemillard2006>{{cite book |last1=McClintock |first1=J. E. |last2=Remillard |first2=R. A. |chapter=Black Hole Binaries |editor1-first=W. |editor1-last=Lewin|editor2-first=M. |editor2-last=van der Klis |title=Compact Stellar X-ray Sources |page=157 |date=2006 |isbn=978-0-521-82659-4 |arxiv=astro-ph/0306213 |bibcode=2006csxs.book..157M}} section 4.1.5.</ref><ref>{{Cite journal |last1=Abramowicz |first1=Marek A. |last2=Fragile |first2=P. Chris |title=Foundations of Black Hole Accretion Disk Theory |journal=Living Reviews in Relativity |date=2013 |volume=16 |issue=1 |article-number=1 |doi=10.12942/lrr-2013-1 |pmid=28179840 |pmc=5256006 |arxiv=1104.5499 |bibcode=2013LRR....16....1A |doi-access=free }}</ref><ref>{{Cite journal |last1=Blaes |first1=Omer |title=General Overview of Black Hole Accretion Theory |journal=Space Science Reviews |date=2014 |volume=183 |issue=1–4 |pages=21–41 |doi=10.1007/s11214-013-9985-6 |arxiv=1304.4879 |bibcode=2014SSRv..183...21B }}</ref><ref name="pt74">{{Cite journal |last1=Page |first1=Don N. |last2=Thorne |first2=Kip S. |title=Disk-Accretion onto a Black Hole. Time-Averaged Structure of Accretion Disk |journal=The Astrophysical Journal |date=1974 |volume=191 |page=499 |doi=10.1086/152990 |bibcode=1974ApJ...191..499P }}</ref> The temperature of these disks can range from thousands to millions of [[Kelvin]], and temperatures can differ throughout a single accretion disk.<ref>{{Cite book |last1=Lasota |first1=Jean-Pierre |title=Astrophysics of Black Holes |chapter=Black Hole Accretion Discs |series=Astrophysics and Space Science Library |date=2016 |volume=440 |pages=1–60 |doi=10.1007/978-3-662-52859-4_1 |arxiv=1505.02172 |isbn=978-3-662-52857-0 }}</ref><ref>{{Cite journal |last1=Beloborodov |first1=A. M. |title=Super-Eddington accretion discs around Kerr black holes |journal=Monthly Notices of the Royal Astronomical Society |date=1998 |volume=297 |issue=3 |pages=739–746 |doi=10.1046/j.1365-8711.1998.01530.x |arxiv=astro-ph/9802129 |bibcode=1998MNRAS.297..739B |doi-access=free }}</ref> Accretion disks can also emit in other parts of the [[electromagnetic spectrum]], depending on the disk's [[turbulence]] and [[magnetization]] and the black hole's mass and angular momentum.<ref name="pt74" /><ref>{{Cite journal |last1=Bisnovatyi-Kogan |first1=Gennady |title=Accretion into Black Hole, and Formation of Magnetically Arrested Accretion Disks |journal=Universe |date=2019 |volume=5 |issue=6 |page=146 |doi=10.3390/universe5060146 |arxiv=1905.13731 |bibcode=2019Univ....5..146B |doi-access=free }}</ref><ref>{{Cite journal |last1=Zakharov |first1=A. F. |last2=Repin |first2=S. V. |title=Model radiation spectrum for an accretion disk near a rotating black hole |journal=Astronomy Reports |date=2002 |volume=46 |issue=5 |pages=360–365 |doi=10.1134/1.1479423 |bibcode=2002ARep...46..360Z }}</ref> 

Accretion disks can be defined as geometrically thin or geometrically thick. Geometrically thin disks are mostly confined to the black hole's equatorial plane and have a well-defined edge at the [[innermost stable circular orbit]] (ISCO), while geometrically thick disks are supported by internal pressure and temperature and can extend inside the ISCO. Disks with high rates of [[electron scattering]] and absorption, appearing bright and [[opaque]], are called ''optically thick''; ''Optically thin'' disks are more [[translucent]] and produce fainter images when viewed from afar.<ref name="wang25">{{Cite journal |last1=Wang |first1=Zi-Liang |title=Exploring the role of accretion disk geometry in shaping black hole shadows |journal=Physical Review D |date=2025 |volume=112 |issue=6 |article-number=064052 |doi=10.1103/fhqj-wgcm |arxiv=2506.21148 |bibcode=2025PhRvD.112f4052W }}</ref> Accretion disks of black holes accreting beyond the [[Eddington limit]] are often referred to as "polish donuts" due to their thick, toroidal shape that resembles that of a [[donut]].<ref>{{Cite journal |last1=Gimeno-Soler |first1=Sergio |last2=Font |first2=José A. |title=Magnetised Polish doughnuts revisited |journal=Astronomy & Astrophysics |date=2017 |volume=607 |pages=A68 |doi=10.1051/0004-6361/201730935 |arxiv=1707.03867 |bibcode=2017A&A...607A..68G }}</ref><ref>{{Cite journal |last1=Qian |first1=Lei |last2=Abramowicz |first2=M. A. |last3=Fragile |first3=P. C. |last4=Horák |first4=J. |last5=Machida |first5=M. |last6=Straub |first6=O. |title=The Polish doughnuts revisited |journal=Astronomy & Astrophysics |date=2009 |volume=498 |issue=2 |pages=471–477 |doi=10.1051/0004-6361/200811518}}</ref><ref>{{Cite book |last1=Abramowicz |first1=M.A. |title=Growing Black Holes: Accretion in a Cosmological Context |chapter=Super-Eddington Black Hole Accretion |series=ESO Astrophysics Symposia |date=2005 |pages=257–273 |doi=10.1007/11403913_49 |isbn=978-3-540-25275-7 }}</ref>

Quasar accretion disks are expected to generally appear blue in color.<ref>{{Cite journal |last1=Kishimoto |first1=Makoto |last2=Antonucci |first2=Robert |last3=Blaes |first3=Omer |last4=Lawrence |first4=Andy |last5=Boisson |first5=Catherine |last6=Albrecht |first6=Marcus |last7=Leipski |first7=Christian |title=The characteristic blue spectra of accretion disks in quasars as uncovered in the infrared |journal=Nature |date=2008 |volume=454 |issue=7203 |pages=492–494 |doi=10.1038/nature07114 |pmid=18650919 |arxiv=0807.3703 |bibcode=2008Natur.454..492K }}</ref> The disk for a stellar black hole, on the other hand, would likely look orange, yellow, or red, with its inner regions being the brightest.<ref>{{Cite journal |last1=Fukue |first1=Jun |last2=Yokoyama |first2=Takushi |title=Color Photographs of an Accretion Disk around a Black Hole |journal=Publications of the Astronomical Society of Japan |date=1988 |volume=40 |pages=15–24 |doi=10.1093/pasj/40.1.15}}</ref> Theoretical research suggests that the hotter a disk is, the bluer it should be, although this is not always supported by observations of real astronomical objects.<ref>{{Cite journal |last1=Bonning |first1=E. W. |last2=Cheng |first2=L. |last3=Shields |first3=G. A. |last4=Salviander |first4=S. |last5=Gebhardt |first5=K. |title=Accretion Disk Temperatures and Continuum Colors in QSOs |journal=The Astrophysical Journal |date=2007 |volume=659 |issue=1 |pages=211–217 |doi=10.1086/510712 |arxiv=astro-ph/0611263 |bibcode=2007ApJ...659..211B }}</ref> Accretion disk colors may also be altered by the [[Doppler effect]], with the part of the disk travelling towards an observer appearing bluer and brighter and the part of the disk travelling away from the observer appearing redder and dimmer.<ref name="scienceofinterstellar" /><ref name="jtft15">{{Cite journal |last1=James |first1=Oliver |last2=Tunzelmann |first2=Eugénie von |last3=Franklin |first3=Paul |last4=Thorne |first4=Kip S. |title=Gravitational lensing by spinning black holes in astrophysics, and in the movie ''Interstellar'' |journal=Classical and Quantum Gravity |date=2015 |volume=32 |issue=6 |doi=10.1088/0264-9381/32/6/065001 |arxiv=1502.03808 |bibcode=2015CQGra..32f5001J }}</ref><ref>{{Cite journal |last1=Guo |first1=Sen |last2=Huang |first2=Yu-Xiang |last3=Cui |first3=Yu-Hao |last4=Han |first4=Yan |last5=Jiang |first5=Qing-Quan |last6=Liang |first6=En-Wei |last7=Lin |first7=Kai |title=Unveiling the unconventional optical signatures of regular black holes within accretion disk |journal=The European Physical Journal C |date=2023 |volume=83 |issue=11 |article-number=1059 |doi=10.1140/epjc/s10052-023-12208-0 |arxiv=2310.20523 |bibcode=2023EPJC...83.1059G }}</ref>

====Relativistic jets====
{{See also|Astrophysical jet}}
[[File:Black Hole Outflows From Centaurus A.jpg |thumb |Relativistic jets from the supermassive black hole in [[Centaurus A]] extend [[perpendicular]]ly from the galaxy.]]
Some black holes have relativistic jets--thin streams of [[plasma (physics)|plasma]] travelling away from the black hole at more than one-tenth of the speed of light.<ref name="mr99">{{Cite journal |last1=Mirabel |first1=I. F. |last2=Rodríguez |first2=L. F. |title=Sources of Relativistic Jets in the Galaxy |journal=Annual Review of Astronomy and Astrophysics |date=1999 |volume=37 |pages=409–443 |doi=10.1146/annurev.astro.37.1.409 |arxiv=astro-ph/9902062 |bibcode=1999ARA&A..37..409M }}</ref>{{refn|group=Note |Relativistic jets do not come from matter from inside of the black hole, but from matter close to the black hole.<ref>{{Cite web |title=Relativistic Jets |url=https://nustar.caltech.edu/page/relativistic-jets |access-date=2025-11-09 |website=NuSTAR}}</ref>}} These jets can extend as far as millions of [[parsec]]s from the black hole itself.<ref>{{Cite journal |last9=Jacob |first9=Joe |last1=Bagchi |first1=Joydeep |last2=Vivek |first2=M. |last3=Vikram |first3=Vinu |last4=Hota |first4=Ananda |last5=Biju |first5=K. G. |last6=Sirothia |first6=S. K. |last7=Srianand |first7=Raghunathan |last8=Gopal-Krishna |title=Megaparsec Relativistic Jets Launched from an Accreting Supermassive Black Hole in an Extreme Spiral Galaxy |journal=The Astrophysical Journal |date=2014 |volume=788 |issue=2 |page=174 |doi=10.1088/0004-637X/788/2/174 |arxiv=1404.6889 |bibcode=2014ApJ...788..174B }}</ref> 

Black holes of any mass can have jets.<ref name="nemmen12">{{Cite journal |last1= Nemmen|first1= R. S.|last2= Georganopoulos|first2= M.|last3= Guiriec|first3= S.|last4= Meyer|first4= E. T.|last5= Gehrels|first5= N.|last6= Sambruna|first6= R. M.|title= A Universal Scaling for the Energetics of Relativistic Jets from Black Hole Systems|journal= Science|date= 2012|volume= 338|issue= 6113|pages= 1445–1448|doi= 10.1126/science.1227416|pmid= 23239730|arxiv= 1212.3343|bibcode= 2012Sci...338.1445N}}</ref> However, they are typically observed around spinning black holes with strongly-magnetized accretion disks.<ref name="bmr18" /><ref>{{Cite journal |last1=Chen 陈 |first1=Yongyun 永云 |last2=Gu 顾 |first2=Qiusheng 秋生 |last3=Fan 樊 |first3=Junhui 军辉 |last4=Zhou 周 |first4=Hongyan 宏岩 |last5=Yuan 袁 |first5=Yefei 业飞 |last6=Gu 顾 |first6=Weimin 为民 |last7=Wu 吴 |first7=Qinwen 庆文 |last8=Xiong 熊 |first8=Dingrong 定荣 |last9=Guo 郭 |first9=Xiaotong 晓通 |last10=Ding 丁 |first10=Nan 楠. |last11=Yu 俞 |first11=Xiaoling 效龄 |title=The Powers of Relativistic Jets Depend on the Spin of Accreting Supermassive Black Holes |journal=The Astrophysical Journal |date=2021 |volume=913 |issue=2 |page=93 |doi=10.3847/1538-4357/abf4ff |arxiv=2104.04242 |bibcode=2021ApJ...913...93C |doi-access=free }}</ref> Relativistic jets were more common in the [[Chronology of the universe#Gravity builds cosmic structure|early universe]], when galaxies and their corresponding supermassive black holes were rapidly gaining mass.<ref name="bmr18">{{Cite journal |last1=Blandford |first1=Roger |last2=Meier |first2=David |last3=Readhead |first3=Anthony |title=Relativistic Jets from Active Galactic Nuclei |journal=Annual Review of Astronomy and Astrophysics |date=2019 |volume=57 |pages=467–509 |doi=10.1146/annurev-astro-081817-051948 |arxiv=1812.06025 |bibcode=2019ARA&A..57..467B }}</ref><ref>{{Cite journal |last1=Ghisellini |first1=G. |last2=Haardt |first2=F. |last3=Ceca |first3=R. Della |last4=Volonteri |first4=M. |last5=Sbarrato |first5=T. |title=The role of relativistic jets in the heaviest and most active supermassive black holes at high redshift |journal=Monthly Notices of the Royal Astronomical Society |date=2013 |volume=432 |issue=4 |pages=2818–2823 |doi=10.1093/mnras/stt637 |doi-access=free }}</ref> All black holes with jets also have an accretion disk, but the jets are usually brighter than the disk.<ref name="mr99" /><ref>{{Cite journal |last1=Ghisellini |first1=G. |last2=Tavecchio |first2=F. |last3=Maraschi |first3=L. |last4=Celotti |first4=A. |last5=Sbarrato |first5=T. |title=The power of relativistic jets is larger than the luminosity of their accretion disks |journal=Nature |date=2014 |volume=515 |issue=7527 |pages=376–378 |doi=10.1038/nature13856 |pmid=25409827 |arxiv=1411.5368 |bibcode=2014Natur.515..376G }}</ref> Supermassive black holes with jets are often called ''[[quasar]]s'', and their stellar-mass companions are referred to as ''[[microquasar]]s''.<ref>{{Cite journal |last1=Meier |first1=David L. |title=The theory and simulation of relativistic jet formation: Towards a unified model for micro- and macroquasars |journal=New Astronomy Reviews |date=2003 |volume=47 |issue=6–7 |pages=667–672 |doi=10.1016/S1387-6473(03)00120-9 |arxiv=astro-ph/0312048 |bibcode=2003NewAR..47..667M }}</ref>

The mechanism of formation of jets is not yet known,<ref name="nemmen12" /> but several options have been proposed. One method proposed to fuel these jets is the [[Blandford-Znajek process]], which suggests that the dragging of [[magnetic field lines]] by a black hole's rotation could launch jets of matter into space.<ref name="lwb00" /><ref>{{Cite journal |last1=Blandford |first1=R. D. |last2=Znajek |first2=R. L. |year=1977 |title=Electromagnetic extraction of energy from Kerr black holes |journal=[[Monthly Notices of the Royal Astronomical Society]] |volume=179 |issue=3 |pages=433 |bibcode=1977MNRAS.179..433B |doi=10.1093/mnras/179.3.433 |doi-access=free |arxiv=astro-ph/0506302}}</ref> The [[Penrose process]], which involves extraction of a black hole's [[rotational energy]], has also been proposed as a potential mechanism of jet propulsion.<ref>{{cite journal |last1=Penrose |first1=R. |year=1969
 |title=Gravitational Collapse: The Role of General Relativity |journal=[[Rivista del Nuovo Cimento]] |volume=1 |pages=252–276 |bibcode=1969NCimR...1..252P}}</ref><ref>{{Cite book |last1=Narayan |first1=Ramesh |last2=McClintock |first2=Jeffrey E. |last3=Tchekhovskoy |first3=Alexander |title=General Relativity, Cosmology and Astrophysics |chapter=Energy Extraction from Spinning Black Holes Via Relativistic Jets |date=2014 |pages=523–535 |doi=10.1007/978-3-319-06349-2_25 |arxiv=1303.3004 |isbn=978-3-319-06348-5 }}</ref>

==== Innermost stable circular orbit (ISCO) ====
{{main|Innermost stable circular orbit}}
[[File:How to Measure the Spin of a Black Hole.jpg|thumb|Since particles in a black hole's accretion disk must orbit at or outside the ISCO, astronomers can observe the properties of accretion disks to determine black hole spins.<ref>{{Cite journal |last1=McClintock |first1=Jeffrey E. |last2=Narayan |first2=Ramesh |last3=Davis |first3=Shane W. |last4=Gou |first4=Lijun |last5=Kulkarni |first5=Akshay |last6=Orosz |first6=Jerome A. |last7=Penna |first7=Robert F. |last8=Remillard |first8=Ronald A. |last9=Steiner |first9=James F. |title=Measuring the spins of accreting black holes |journal=Classical and Quantum Gravity |date=2011 |volume=28 |issue=11 |doi=10.1088/0264-9381/28/11/114009 |arxiv=1101.0811 |bibcode=2011CQGra..28k4009M }}</ref>]]
In [[Newton's law of universal gravitation|Newtonian gravity]], [[test particle]]s can stably orbit at arbitrary distances from a central object. In general relativity, however, there exists a smallest possible radius for which a massive particle can orbit stably. Any infinitesimal inward [[perturbation (astronomy)|perturbations]] to this orbit will lead to the particle [[orbital decay|spiraling into]] the black hole, and any outward perturbations will, depending on the energy, cause the particle to spiral in, move to a stable orbit further from the black hole, or escape to infinity. This orbit is called the '''innermost stable circular orbit''', or ISCO.<ref>{{harvnb|Misner|Thorne|Wheeler|1973|loc=Box 25.6}}</ref><ref name="jtb15">{{Cite journal |last1=Jefremov |first1=Paul I. |last2=Tsupko |first2=Oleg Yu. |last3=Bisnovatyi-Kogan |first3=Gennady S. |title=Innermost stable circular orbits of spinning test particles in Schwarzschild and Kerr space-times |journal=Physical Review D |date=2015 |volume=91 |issue=12 |article-number=124030 |doi=10.1103/PhysRevD.91.124030 |arxiv=1503.07060 |bibcode=2015PhRvD..91l4030J }}</ref> The location of the ISCO depends on the spin of the black hole and the [[spin (physics)|spin]] of the particle itself. In the case of a Schwarzschild black hole (spin zero) and a particle without spin, the location of the ISCO is:
<math display="block">r_{\rm ISCO}=3 \, r_\text{s}=\frac{6 \, GM}{c^2}.</math><ref name="Bardeen1972"/>
The radius of this orbit changes slightly based on particle spin.<ref name="zwgsl18">{{Cite journal |last1=Zhang |first1=Yu-Peng |last2=Wei |first2=Shao-Wen |last3=Guo |first3=Wen-Di |last4=Sui |first4=Tao-Tao |last5=Liu |first5=Yu-Xiao |title=Innermost stable circular orbit of spinning particle in charged spinning black hole background |journal=Physical Review D |date=2018 |volume=97 |issue=8 |article-number=084056 |doi=10.1103/PhysRevD.97.084056 |arxiv=1711.09361 |bibcode=2018PhRvD..97h4056Z }}</ref><ref>{{Cite journal |last1=Tsupko |first1=O. Yu. |last2=Bisnovatyi-Kogan |first2=G. S. |last3=Jefremov |first3=P. I. |title=Parameters of innermost stable circular orbits of spinning test particles: Numerical and analytical calculations |journal=Gravitation and Cosmology |date=2016 |volume=22 |issue=2 |pages=138–147 |doi=10.1134/S0202289316020158 |arxiv=1605.04189 |bibcode=2016GrCo...22..138T }}</ref> The ISCO moves inward for charged black holes.<ref name="zwgsl18" /> For spinning black holes, the ISCO is moved inwards for particles orbiting in the same direction that the black hole is spinning ([[retrograde and prograde motion|prograde]]) and outwards for particles orbiting in the opposite direction (retrograde).<ref name="jtb15" /> For example, the ISCO for a particle orbiting retrograde can be as far out as about <math>9r_\text{s}</math>, while the ISCO for a particle orbiting prograde can be as close as at the event horizon itself.<ref name="jtb15" /><ref>{{Cite book |last1=Jefremov |first1=Paul I. |last2=Tsupko |first2=Oleg Yu. |last3=Bisnovatyi-Kogan |first3=Gennady S. |title=The Fourteenth Marcel Grossmann Meeting |chapter=Spin-induced changes in the parameters of ISCO in Kerr spacetime |date=2017 |pages=3715–3721 |doi=10.1142/9789813226609_0486 |isbn=978-981-322-659-3 }}</ref>

==== Plunging region ====
{{main|Plunging region}}
The final observable region of spacetime around a black hole is called the plunging region. In this area it is no longer possible for matter to follow circular orbits or to stop a final descent into the black hole. Instead, it will rapidly plunge toward the black hole at close to the speed of light, growing increasingly hot and producing a characteristic, detectable [[thermal radiation|thermal emission]].<ref>{{cite web |title=First proof of black hole 'plunging regions' |url=https://www.physics.ox.ac.uk/news/first-proof-black-hole-plunging-regions |department=Department of Physics |publisher=[[University of Oxford]] |date=16 May 2024}}</ref><ref>{{cite journal |last1=Mummery |first1=Andrew |last2=Ingram |first2=Adam |last3=Davis |first3=Shane |last4=Fabian |first4=Andrew |title=Continuum emission from within the plunging region of black hole discs |journal=Monthly Notices of the Royal Astronomical Society |volume=531 |issue=1 |pages=366–386 |date=June 2024 |doi=10.1093/mnras/stae1160|doi-access=free |arxiv=2405.09175 }}</ref><ref>{{Cite journal |last1=Machida |first1=Mami |last2=Matsumoto |first2=Ryoji |title=Global Three-dimensional Magnetohydrodynamic Simulations of Black Hole Accretion Disks: X-Ray Flares in the Plunging Region |journal=The Astrophysical Journal |date=2003 |volume=585 |issue=1 |pages=429–442 |doi=10.1086/346070 |arxiv=astro-ph/0211240 |bibcode=2003ApJ...585..429M }}</ref> However, light and thermal radiation emitted from this region can still escape from the black hole's gravitational pull.<ref name="prisco">{{Cite web |title=Study proves black holes have a 'plunging region,' just as Einstein predicted |url=https://www.cnn.com/2024/05/17/world/black-holes-einstein-plunging-region-scn |last=Prisco |first=Jacopo |website=[[CNN]] |date=17 May 2024}}</ref>

==== Photon sphere ====
{{main|Photon sphere}}
[[File:Photon capture by a Schwarzschild black hole - video.ogg|thumb|thumbtime=6|Video of a photon being captured by a Schwarzschild black hole |alt=A photon (small, black with yellow trail) being captured in the [[photon sphere]] of a Schwarzschild black hole (large, black, center)]]

The [[photon sphere]] is a spherical boundary where photons that move on tangents to that sphere would be trapped in an unstable, circular orbit around the black hole.<ref name="Cramer 1997">{{cite journal |last=Cramer |first=Claes R. |date=1997 |title=Using the Uncharged Kerr Black Hole as a Gravitational Mirror |journal=General Relativity and Gravitation |volume=29 |issue=4 |pages=445–454 |doi=10.1023/A:1018878515046 |arxiv=gr-qc/9510053 |bibcode=1997GReGr..29..445C |s2cid=9517046}}</ref>
For Schwarzschild black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius.<ref name="ll19">{{Cite journal |last1=Lü |first1=H. |last2=Lyu |first2=Hong-Da |title=Schwarzschild black holes have the largest size |journal=Physical Review D |date=2020 |volume=101 |issue=4 |article-number=044059 |doi=10.1103/PhysRevD.101.044059 |arxiv=1911.02019 |bibcode=2020PhRvD.101d4059L }}</ref><ref name="qiao22">{{Cite journal |last1=Qiao |first1=Chen-Kai |title=Curvatures, photon spheres, and black hole shadows |journal=Physical Review D |date=2022 |volume=106 |issue=8 |article-number=084060 |doi=10.1103/PhysRevD.106.084060 |arxiv=2208.01771 |bibcode=2022PhRvD.106h4060Q }}</ref> Non-Schwarzschild black holes have a photon sphere radius at least 1.5 times that of the event horizon, but the photon sphere's radius is never larger than the radius of the black hole's shadow.<ref name="ll19" /><ref>{{Cite journal |last1=Ma |first1=Liang |last2=Lü |first2=H. |title=Bounds on photon spheres and shadows of charged black holes in Einstein-Gauss-Bonnet-Maxwell gravity |journal=Physics Letters B |date=2020 |volume=807 |article-number=135535 |doi=10.1016/j.physletb.2020.135535 |arxiv=1912.05569 |bibcode=2020PhLB..80735535M }}</ref> Their orbits would likely be [[instability|unstable]], so any small perturbation, such as a particle of infalling matter, would cause an instability that would grow over time. This would either set the photon on an outward trajectory, causing it to escape from the black hole's orbit, or on an inward spiral, where it would eventually cross the event horizon.<ref name="ll19" /><ref name="qiao22" /><ref name=prd84_6>{{cite journal |last1=Nitta |first1=Daisuke |last2=Chiba |first2=Takeshi |last3=Sugiyama |first3=Naoshi |title=Shadows of colliding black holes |journal=Physical Review D |volume=84 |issue=6 |article-number=063008 |date=September 2011 |doi=10.1103/PhysRevD.84.063008 |bibcode=2011PhRvD..84f3008N |arxiv=1106.2425 |s2cid=119264596}}</ref>

For a rotating, uncharged black hole, the radius of the photon sphere depends on the spin parameter and whether the photon is orbiting prograde or retrograde.<ref name="Bardeen1972">{{cite journal|last1=Bardeen|first1=James M.|last2=Press|first2=William H.|last3=Teukolsky|first3=Saul A.|date=1 December 1972|title=Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation|journal=The Astrophysical Journal|volume=178|pages=347–370|doi=10.1086/151796|bibcode=1972ApJ...178..347B}}</ref> For a photon orbiting prograde, the photon sphere will be 1-3 Schwarzschild radii from the center of the black hole, while for a photon orbiting retrograde, the photon sphere will be between 3-5 Schwarzschild radii from the center of the black hole. The exact location of the photon sphere depends on the [[magnitude (mathematics)#numbers|magnitude]] of the black hole's rotation.<ref>{{Cite journal |last1=Teo |first1=Edward |title=Spherical Photon Orbits Around a Kerr Black Hole |journal=General Relativity and Gravitation |date=2003 |volume=35 |issue=11 |pages=1909–1926 |doi=10.1023/A:1026286607562 |bibcode=2003GReGr..35.1909T |url=http://scholarbank.nus.edu.sg/handle/10635/97985 }}</ref> For a charged, nonrotating black hole, there will only be one photon sphere, and the radius of the photon sphere will decrease for increasing black hole charge.<ref>{{Cite journal |last1=Heydarzade |first1=Yaghoub |last2=Vertogradov |first2=Vitalii |title=Dynamical photon spheres in charged black holes and naked singularities |journal=The European Physical Journal C |date=2024 |volume=84 |issue=6 |article-number=582 |doi=10.1140/epjc/s10052-024-12945-w |arxiv=2311.08930 |bibcode=2024EPJC...84..582H }}</ref> For non-[[extremal black hole|extremal]], charged, rotating black holes, there will always be two photon spheres, with the exact radii depending on the parameters of the black hole.<ref>{{Cite journal |last1=Chen |first1=Ying-Xuan |last2=Huang |first2=Jia-Hui |last3=Jiang |first3=Haoxiang |title=Radii of spherical photon orbits around Kerr-Newman black holes |journal=Physical Review D |date=2023 |volume=107 |issue=4 |article-number=044066 |doi=10.1103/PhysRevD.107.044066 |arxiv=2210.08509 |bibcode=2023PhRvD.107d4066C }}</ref>

While light can still escape from the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Therefore, any light that reaches an outside observer from the photon sphere must have been emitted by objects between the photon sphere and the event horizon.<ref name=prd84_6 />

=== Event horizon ===
{{main|Event horizon}}
{{multiple image
| align             = right
| direction         = vertical
| width             = 300
| image1            = BH-no-escape-1.svg
| caption1          = Far away from the black hole, a particle can move in any direction, as illustrated by the set of arrows. It is restricted only by the speed of light.
| image2            = BH-no-escape-2.svg
| caption2          = Closer to the black hole, spacetime starts to deform. There are more paths going towards the black hole than paths moving away.{{refn|The set of possible paths, or more accurately the future [[light cone]] containing all possible [[world line]]s (in this diagram the light cone is represented by the V-shaped region bounded by arrows representing light ray world lines), is tilted in this way in [[Eddington–Finkelstein coordinates]] (the diagram is a "cartoon" version of an Eddington–Finkelstein coordinate diagram), but in other coordinates the light cones are not tilted in this way, for example in [[Schwarzschild coordinates]] they narrow without tilting as one approaches the event horizon, and in [[Kruskal–Szekeres coordinates]] the light cones do not change shape or orientation at all.<ref>{{harvnb|Misner|Thorne|Wheeler|1973|p=848}}</ref>|group="Note"}}
| image3            = BH-no-escape-3.svg
| caption3          = Inside of the event horizon, all paths bring the particle closer to the centre of the black hole. It is no longer possible for the particle to escape.
}}

The defining feature of a black hole is the existence of an event horizon, a boundary in [[spacetime]] through which matter and light can pass only inward towards the center of the black hole. Nothing, not even light, can escape from inside the event horizon.<ref>{{cite book |title=The New Physics |edition=illustrated |first1=Paul |last1=Davies |publisher=Cambridge University Press |year=1992 |isbn=978-0-521-43831-5 |page=26 |url=https://books.google.com/books?id=akb2FpZSGnMC |access-date=25 September 2020 |archive-date=17 August 2021 |archive-url=https://web.archive.org/web/20210817161727/https://books.google.com/books?id=akb2FpZSGnMC |url-status=live }} [https://books.google.com/books?id=akb2FpZSGnMC&pg=PA26 Extract of page 26] {{Webarchive|url=https://web.archive.org/web/20210815222341/https://books.google.com/books?id=akb2FpZSGnMC&pg=PA26 |date=15 August 2021 }}</ref><ref>{{cite book |title=A Student's Guide to the Mathematics of Astronomy |edition=illustrated |first1=Daniel |last1=Fleisch |first2=Julia |last2=Kregenow |publisher=Cambridge University Press |year=2013 |isbn=978-1-107-03494-5 |page=168 |url=https://books.google.com/books?id=x4gaBQAAQBAJ |access-date=25 September 2020 |archive-date=17 August 2021 |archive-url=https://web.archive.org/web/20210817045139/https://books.google.com/books?id=x4gaBQAAQBAJ |url-status=live }} [https://books.google.com/books?id=x4gaBQAAQBAJ&pg=PA168 Extract of page 168] {{Webarchive|url=https://web.archive.org/web/20210817113029/https://books.google.be/books?id=x4gaBQAAQBAJ&pg=PA168 |date=17 August 2021 }}</ref> The event horizon is referred to as such because if an event occurs within the boundary, information from that event cannot reach or affect an outside observer, making it impossible to determine whether such an event occurred.<ref>{{harvnb|Wheeler|2007|p=179}}</ref>

As predicted by general relativity, the presence of a mass deforms spacetime in such a way that the paths taken by particles bend towards the mass.<ref>{{harvnb|Carroll|2004|loc=Ch. 5.4 and 7.3}}</ref> At the event horizon of a black hole, this deformation becomes so strong that there are no paths that<!--to avoid false positives in search for 'that led/lead' typo--> lead away from the black hole.<ref>{{cite web |title=Singularities and Black Holes > Lightcones and Causal Structure |url=https://plato.stanford.edu/entries/spacetime-singularities/lightcone.html |website=plato.stanford.edu |publisher=[[Stanford Encyclopedia of Philosophy]] |access-date=11 March 2018 |archive-date=17 May 2019 |archive-url=https://web.archive.org/web/20190517122738/https://plato.stanford.edu/entries/spacetime-singularities/lightcone.html |url-status=live }}</ref>

To a distant observer, a clock near a black hole would appear to tick more slowly than one further from the black hole.<ref>{{harvnb|Carroll|2004|p=217}}</ref> This effect, known as [[gravitational time dilation]], would also cause an object falling into a black hole to appear to slow as it approached the event horizon, never quite reaching the horizon from the perspective of an outside observer.<ref>{{harvnb|Carroll|2004|p=218}}</ref> All processes on this object would appear to slow down, and any light emitted by the object to appear redder and dimmer, an effect known as [[gravitational redshift]].<ref>{{cite web |url=http://nrumiano.free.fr/Estars/int_bh.html |title=Inside a black hole |website=Knowing the universe and its secrets |access-date=26 March 2009 |archive-url=https://web.archive.org/web/20090423053437/http://nrumiano.free.fr/Estars/int_bh.html |archive-date=23 April 2009 }}</ref> Eventually, the falling object would fade away until it could no longer be seen. Typically, this process would happen very rapidly, with an object disappearing from view within less than a second.<ref>{{cite web |title=What happens to you if you fall into a black hole |url=http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html |website=math.ucr.edu |publisher=[[John Baez]] |access-date=11 March 2018 |archive-date=13 February 2019 |archive-url=https://web.archive.org/web/20190213124648/http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html |url-status=live }}</ref>

On the other hand, an observer falling into a black hole would not notice any of these effects as they cross the event horizon. Their own clocks appear to them to tick normally, and they cross the event horizon after a finite time without noting any singular behaviour. In [[general relativity]], it is impossible to determine the location of the event horizon from local observations, due to Einstein's [[equivalence principle]].<ref>{{harvnb|Carroll|2004|p=222}}</ref><ref>{{cite news |title=Watch: Three Ways an Astronaut Could Fall Into a Black Hole |url=https://news.nationalgeographic.com/news/2014/01/140130-black-holes-stephen-hawking-work-space-astronomy/ |access-date=13 March 2018 |date=1 February 2014 |archive-date=15 April 2019 |archive-url=https://web.archive.org/web/20190415101947/https://news.nationalgeographic.com/news/2014/01/140130-black-holes-stephen-hawking-work-space-astronomy/ }}</ref> Although the exterior universe would appear brighter, [[blueshift|bluer]], and in fast-motion as the observer fell in, this effect would be finite, and could even be cancelled out if the observer were travelling at sufficiently fast speeds.<ref name="scienceofinterstellar"/>

For non-rotating black holes, the geometry of the event horizon is precisely spherical, while for rotating black holes, the event horizon is [[oblate spheroid|oblate]].<ref name= "Smarr1973">{{cite journal|last1= Smarr|first1= L.|title= Surface Geometry of Charged Rotating Black Holes |journal= Physical Review D|volume= 7|issue= 2|year= 1973|pages= 289–295|doi= 10.1103/PhysRevD.7.289|bibcode= 1973PhRvD...7..289S}}</ref><ref name= "Wiltshire2009">{{cite book|author= Visser, M.|editor1= Wiltshire, D.L.|editor2= Visser, M.|editor3= Scott, S.M.|title= Horizon geometry for Kerr black holes with synchronized hair|url= https://books.google.com/books?id=wymJBq_80Q0C|chapter= The Kerr spacetime: A brief introduction|journal= Physical Review D|date= 22 January 2009|volume= 97|issue= 12|article-number= 124012|publisher= Cambridge University Press|doi= 10.1103/PhysRevD.97.124012|isbn= 978-0-521-88512-6|arxiv= 0706.0622|bibcode= 2018PhRvD..97l4012D|access-date= 12 January 2020|archive-date= 20 May 2020|archive-url= https://web.archive.org/web/20200520134643/https://books.google.com/books?id=wymJBq_80Q0C|url-status= live}}</ref><ref name= "Delgado2018">{{cite journal|last1= Delgado|first1= J.F. M.|last2= Herdeiro|first2= C.A. R.|last3= Radu|first3= E.|title= Horizon geometry for Kerr black holes with synchronized hair|journal= Physical Review D|volume= 97|issue= 12|article-number= 124012|year= 2018|doi= 10.1103/PhysRevD.97.124012|bibcode= 2018PhRvD..97l4012D|hdl= 10773/24121|arxiv= 1804.04910|s2cid= 55732213}}</ref>

=== Internal geometry ===
====Cauchy horizon====
{{Main article|Cauchy horizon}}
Black holes that are rotating and/or charged have an inner horizon, often called the Cauchy horizon, inside of the black hole.<ref name="hp98">{{Cite journal |last1=Hod |first1=Shahar |last2=Piran |first2=Tsvi |title=The Inner Structure of Black Holes |journal=General Relativity and Gravitation |date=1998 |volume=30 |issue=11 |pages=1555–1562 |doi=10.1023/A:1026654519980 |arxiv=gr-qc/9902008 |bibcode=1998GReGr..30.1555H }}</ref><ref name="pi90">{{Cite journal |last1=Poisson |first1=Eric |last2=Israel |first2=Werner |title=Internal structure of black holes |journal=Physical Review D |date=1990 |volume=41 |issue=6 |pages=1796–1809 |doi=10.1103/PhysRevD.41.1796 |pmid=10012548 |bibcode=1990PhRvD..41.1796P }}</ref> The inner horizon is divided up into two segments: an ingoing section and an outgoing section.<ref name="st14">{{Cite journal |last1=Scheel |first1=M. A. |last2=Thorne |first2=K. S. |title=Geometrodynamics: The nonlinear dynamics of curved spacetime |journal=Physics-Uspekhi |date=2014 |volume=57 |issue=4 |pages=342–351 |doi=10.3367/UFNe.0184.201404b.0367 |arxiv=1706.09078 |bibcode=2014PhyU...57..342S }}</ref>

At the ingoing section of the Cauchy horizon, radiation and matter that fall into the black hole would build up at the horizon, causing the curvature of spacetime to go to infinity. This would cause an observer falling in to experience tidal forces.<ref name="hp98" /><ref name="pi90" /><ref name="st14" /> This phenomenon is often called [[mass inflation]], since it is associated with a [[parameter]] dictating the black hole's internal mass [[exponential growth|growing exponentially]],<ref name="pi90" /><ref name="mo12">{{Cite journal |last1=Marolf |first1=Donald |last2=Ori |first2=Amos |title=Outgoing gravitational shock wave at the inner horizon: The late-time limit of black hole interiors |journal=Physical Review D |date=2012 |volume=86 |issue=12 |article-number=124026 |doi=10.1103/PhysRevD.86.124026 |arxiv=1109.5139 |bibcode=2012PhRvD..86l4026M }}</ref> and the buildup of tidal forces is called the mass-inflation singularity<ref name="ori91">{{Cite journal |last1=Ori |first1=Amos |title=Inner structure of a charged black hole: An exact mass-inflation solution |journal=Physical Review Letters |date=1991 |volume=67 |issue=7 |pages=789–792 |doi=10.1103/PhysRevLett.67.789 |pmid=10044989 |bibcode=1991PhRvL..67..789O }}</ref><ref name="st14" /> or Cauchy horizon singularity.<ref>{{Cite journal |last1=Burko |first1=Lior M. |title=Structure of the Black Hole's Cauchy-Horizon Singularity |journal=Physical Review Letters |date=1997 |volume=79 |issue=25 |pages=4958–4961 |doi=10.1103/PhysRevLett.79.4958 |arxiv=gr-qc/9710112 |bibcode=1997PhRvL..79.4958B }}</ref><ref>{{Cite journal |last1=Burko |first1=Lior M. |last2=Khanna |first2=Gaurav |last3=Zenginoǧlu |first3=Anıl |title=Cauchy-horizon singularity inside perturbed Kerr black holes |journal=Physical Review D |date=2016 |volume=93 |issue=4 |article-number=041501 |doi=10.1103/PhysRevD.93.041501 |arxiv=1601.05120 |bibcode=2016PhRvD..93d1501B }}</ref> Some physicists have argued that in realistic black holes, accretion and Hawking radiation would stop mass inflation from occurring.<ref>{{Cite journal |last1=Hamilton |first1=Andrew J. S. |title=Mass inflation followed by Belinskii-Khalatnikov-Lifshitz collapse inside accreting, rotating black holes |journal=Physical Review D |date=2017 |volume=96 |issue=8 |article-number=084041 |doi=10.1103/PhysRevD.96.084041 |arxiv=1703.01921 |bibcode=2017PhRvD..96h4041H }}</ref><ref>{{Cite journal |last1=Barceló |first1=Carlos |last2=Boyanov |first2=Valentin |last3=Carballo-Rubio |first3=Raúl |last4=Garay |first4=Luis J. |title=Classical mass inflation versus semiclassical inner horizon inflation |journal=Physical Review D |date=2022 |volume=106 |issue=12 |article-number=124006 |doi=10.1103/PhysRevD.106.124006 |arxiv=2203.13539 |bibcode=2022PhRvD.106l4006B }}</ref>

At the outgoing section of the inner horizon, infalling radiation would [[backscatter]] off of the black hole's spacetime curvature and travel outward, building up at the outgoing Cauchy horizon. This would cause an infalling observer to experience a gravitational [[shock wave]] and tidal forces as the spacetime curvature at the horizon grew to infinity. This buildup of tidal forces is called the [[shock singularity]].<ref name="mo12" /><ref name="st14" />

Both of these singularities are [[Penrose-Hawking singularity theorems#Singularities|weak]], meaning that an object crossing them would only be deformed a finite amount by tidal forces, even though the spacetime curvature would still be infinite at the singularity. This is as opposed to a [[Penrose-Hawking singularity theorems#Singularities|strong singularity]], where an object hitting the singularity would be stretched and squeezed by an infinite amount.<ref name="hp98" /><ref name="ori91" /><ref name="mo12" /> They are also [[Penrose-Hawking singularity theorems#Singularities|null singularities]], meaning that a photon could travel [[parallel (geometry)|parallel]] to the them without ever being intercepted.<ref name="st14" />

==== Singularity ====
{{main|Gravitational singularity}}
Mathematical models of black holes based on general relativities have [[gravitational singularity|singularities]] at their centers—points where the curvature of spacetime becomes infinite, and [[geodesic]]s terminate within a finite [[proper time]]. However, it is unknown whether these singularities truly exist in real black holes.<ref name="cd22">{{Cite book |title=The Foundations of Spacetime Physics |last1=Crowther |first1=Karen |date=2022-09-29 |isbn=9781003219019 |location=New York |url=https://philarchive.org/archive/CROFAT-5 |last2=De Haro |first2=Sebastian |editor-last=Vassallo |editor-first=Antonio |chapter=Four Attitudes Towards Singularities in the Search for a Theory of Quantum Gravity |doi=10.4324/9781003219019 |arxiv=2208.05946 }}</ref> Some physicists believe that singularities do not exist, and that their existence, which would make spacetime [[causality (physics)|unpredictable]], signals a breakdown of general relativity and a need for a more complete understanding of [[quantum gravity]].<ref>{{Cite journal |last1=Alesci |first1=Emanuele |last2=Bahrami |first2=Sina |last3=Pranzetti |first3=Daniele |title=Quantum gravity predictions for black hole interior geometry |journal=Physics Letters B |date=2019 |volume=797 |article-number=134908 |doi=10.1016/j.physletb.2019.134908 |arxiv=1904.12412 |bibcode=2019PhLB..79734908A }}</ref><ref>{{Cite journal |last1=Koshelev |first1=Alexey S. |last2=Tokareva |first2=Anna |title=Nonperturbative quantum gravity denounces singular black holes |journal=Physical Review D |date=2025 |volume=111 |issue=8 |article-number=086026 |doi=10.1103/PhysRevD.111.086026 |bibcode=2025PhRvD.111h6026K |doi-access=free }}</ref><ref>{{Cite journal |last1=Olmedo |first1=Javier |last2=Saini |first2=Sahil |last3=Singh |first3=Parampreet |title=From black holes to white holes: A quantum gravitational, symmetric bounce |journal=Classical and Quantum Gravity |date=2017 |volume=34 |issue=22 |doi=10.1088/1361-6382/aa8da8 |arxiv=1707.07333 |bibcode=2017CQGra..34v5011O }}</ref> Others believe that such singularities could be resolved within the current framework of physics, without having to introduce quantum gravity.<ref name="cd22" /> There are also physicists, including Kip Thorne<ref name="scienceofinterstellar" /> and [[Charles Misner]],<ref>{{Cite journal |last1=Misner |first1=Charles W. |title=Absolute Zero of Time |journal=Physical Review |date=1969 |volume=186 |issue=5 |pages=1328–1333 |doi=10.1103/PhysRev.186.1328 |bibcode=1969PhRv..186.1328M }}</ref> who believe that not all singularities can be resolved, and that some likely still exist in the real universe despite the effects of quantum gravity.<ref name="cd22" /><ref name="dlc07">{{Cite journal |last1=Doran |first1=Rosa |last2=Lobo |first2=Francisco S. N. |last3=Crawford |first3=Paulo |title=Interior of a Schwarzschild Black Hole Revisited |journal=Foundations of Physics |date=2008 |volume=38 |issue=2 |pages=160–187 |doi=10.1007/s10701-007-9197-6 |arxiv=gr-qc/0609042 |bibcode=2008FoPh...38..160D }}</ref> Finally, still others believe that singularities do not exist, and that their existence in general relativity does not matter, since general relativity is already believed to be an incomplete theory.<ref name="cd22" />

According to general relativity, every black hole has a singularity inside.<ref name="Carroll 2004 205">{{harvnb|Carroll|2004|p=205}}</ref><ref name="hp70">{{Cite journal |last1=Hawking |first1=S. W. |last2=Penrose |first2=R. |title=The singularities of gravitational collapse and cosmology |journal=Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences |date=1970 |volume=314 |issue=1519 |pages=529–548 |doi=10.1098/rspa.1970.0021 |bibcode=1970RSPSA.314..529H }}</ref> For a non-rotating black hole, this region takes the shape of a single point; for a rotating black hole it is smeared out to form a [[ring singularity]] that lies in the plane of rotation.<ref>{{harvnb|Carroll|2004|pp=264–265}}</ref> In both cases, the singular region has zero volume. All of the mass of the black hole ends up in the singularity.<ref>{{harvnb|Carroll|2004|p=252}}</ref> Since the singularity has nonzero mass in an infinitely small space, it can be thought of as having infinite [[mass density|density]].<ref>{{cite news |title=Sizes of Black Holes? How Big is a Black Hole? |url=https://www.skyandtelescope.com/astronomy-resources/how-big-is-a-black-hole/ |access-date=9 October 2018 |work=[[Sky & Telescope]] |date=22 July 2014 |archive-date=3 April 2019 |archive-url=https://web.archive.org/web/20190403035741/https://www.skyandtelescope.com/astronomy-resources/how-big-is-a-black-hole/ |url-status=live }}</ref>

[[File:BKLChaotic.gif|thumb|Chaotic oscillations of spacetime experienced by an object approaching a gravitational singularity]]
[[File:Sunbeam Mixmaster 03.jpg|thumb|A Mixmaster electric mixer]]

Observers falling into a Schwarzschild black hole (i.e., non-rotating and not charged) cannot avoid being carried into the singularity once they cross the event horizon.<ref>{{cite journal |last1=Lewis |first1=G. F. |last2=Kwan |first2=J. |title=No Way Back: Maximizing Survival Time Below the Schwarzschild Event Horizon |url=https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/no-way-back-maximizing-survival-time-below-the-schwarzschild-event-horizon/2A1CCF5CB13E7BEFA6441B3038C635A3 |journal=Publications of the Astronomical Society of Australia |volume=24 |issue=2 |pages=46–52 |date=2007 |doi=10.1071/AS07012 |arxiv=0705.1029 |bibcode=2007PASA...24...46L |s2cid=17261076}}</ref><ref>{{Cite journal |last1=Toporensky |first1=Alexei |last2=Popov |first2=Sergei |title=How to Delay Death and Look Further into the Future if You Fall into a Black Hole |journal=Resonance |date=2023 |url=https://link.springer.com/article/10.1007/s12045-023-1602-8 |volume=28 |issue=5 |pages=737–749 |doi=10.1007/s12045-023-1602-8|url-access=subscription }}</ref> As they fall further into the black hole, they will be torn apart by the growing [[tidal force]]s in a process sometimes referred to as [[spaghettification]] or the "noodle effect". Eventually, they will reach the singularity and be crushed into an infinitely small point.<ref>{{harvnb|Wheeler|2007|p=182}}</ref>

Before the 1970s, most physicists believed that the interior of a Schwarzschild black hole curved inwards towards a sharp point at the singularity. However, in the late 1960s, Soviet physicists Vladimir Belinskii, Isaak Khalatnikov, and Evgeny Lifshitz discovered that this model was only true when the spacetime inside the black hole had not been perturbed. Any perturbations, such as those caused by matter or radiation falling in, would cause space to [[BKL singularity|oscillate chaotically]] near the singularity. Any matter falling in would experience intense tidal forces rapidly changing in direction, all while being compressed into an increasingly small volume. Physicists termed these oscillations "[[Mixmaster universe|Mixmaster dynamics]]", after a [[Sunbeam Products|brand of mixer]] that was popular at the time that Belinskii, Khalatnikov, and Lifshitz made their discovery, because they have a similar effect on matter near a singularity as an electric mixer would have on dough.<ref>{{Cite book |last1=Belinskii |first1=V.A. |last2=Lifshitz |first2=E.M. |last3=Khalatnikov |first3=I.M. |last4=Agyei |first4=A.K. |title=Perspectives in Theoretical Physics |chapter=The oscillatory mode of approach to a singularity in homogeneous cosmological models with rotating axes |date=1992 |pages=677–689 |doi=10.1016/B978-0-08-036364-6.50048-X |isbn=978-0-08-036364-6 }}</ref><ref name="scienceofinterstellar">{{Cite book |title=The Science of Interstellar |last=Thorne |first=Kip |date=7 November 2014 |publisher=W. W. Norton & Company |isbn=978-0-393-35137-8}}</ref><ref>{{Cite web |title=Of singularities and breadmaking |url=https://www.einstein-online.info/en/spotlight/singularities_bkl/ |last=Garfinkle |first=David |url-status=live |archive-url=https://web.archive.org/web/20250709022836/https://www.einstein-online.info/en/spotlight/singularities_bkl/ |archive-date=9 July 2025 |access-date=14 October 2025 |website=Einstein Online |year=2007}}</ref>

In the case of a charged (Reissner–Nordström) or rotating (Kerr) black hole, it is possible to avoid the singularity. Extending these solutions as far as possible reveals the hypothetical possibility of exiting the black hole into a different spacetime with the black hole acting as a [[wormhole]].<ref>{{harvnb|Carroll|2004|pp=257–259 and 265–266}}</ref> The possibility of travelling to another universe is, however, only theoretical, since any perturbation would destroy this possibility.<ref>{{cite journal |title=Black holes: the inside story |first1=S. |last1=Droz |first2=W. |last2=Israel |first3=S. M. |last3=Morsink |journal=Physics World |volume=9 |issue=1 |pages=34–37 |date=1996|bibcode=1996PhyW....9...34D |doi=10.1088/2058-7058/9/1/26}}</ref> It also appears to be possible to follow [[closed timelike curve]]s (returning to one's own past) around the Kerr singularity, which leads to problems with [[causality (physics)|causality]] like the [[grandfather paradox]].<ref>{{harvnb|Carroll|2004|p=266}}</ref><ref name="thorne93">{{Cite conference |title=Closed Timelike Curves |conference=General relativity and gravitation |last=Thorne |first=Kip S. |url=https://www.its.caltech.edu/~kip/scripts/ClosedTimelikeCurves-II121.pdf |author-link=Kip Thorne |year=1993}}</ref> However, processes inside the black hole, such as quantum gravity effects or mass inflation, might prevent closed timelike curves from arising.<ref name="thorne93" />

Some models of gravity seeking to solve technical issues with general relativity do not include black hole singularities. These theoretical black holes without singularities are called ''regular'', or ''nonsingular'', black holes.<ref>{{Cite journal |last1=Lan |first1=Chen |last2=Yang |first2=Hao |last3=Guo |first3=Yang |last4=Miao |first4=Yan-Gang |title=Regular Black Holes: A Short Topic Review |journal=International Journal of Theoretical Physics |date=2023 |volume=62 |issue=9 |article-number=202 |doi=10.1007/s10773-023-05454-1 |arxiv=2303.11696 |bibcode=2023IJTP...62..202L }}</ref><ref>{{Cite journal |last1=Olmo |first1=Gonzalo |last2=Rubiera-Garcia |first2=Diego |title=Nonsingular Black Holes in ƒ (R) Theories |journal=Universe |date=2015 |volume=1 |issue=2 |pages=173–185 |doi=10.3390/universe1020173 |arxiv=1509.02430 |bibcode=2015Univ....1..173O |doi-access=free }}</ref> For example, the [[Fuzzball (string theory)|fuzzball]] model, based on string theory, states that black holes are actually made up of [[quantum state|quantum microstate]]s and need not have a singularity or an event horizon.<ref>{{cite journal |last=Mathur |first=Samir D. |title=The fuzzball proposal for black holes: an elementary review |journal=Fortschritte der Physik |volume=53 |issue=7–8 |page=793 |date=2005 |doi=10.1002/prop.200410203 |arxiv=hep-th/0502050 |bibcode=2005ForPh..53..793M |s2cid=15083147}}</ref><ref>{{Cite journal |last1=Avery |first1=Steven G. |last2=Chowdhury |first2=Borun D. |last3=Puhm |first3=Andrea |title=Unitarity and fuzzball complementarity: "Alice fuzzes but may not even know it!" |journal=Journal of High Energy Physics |date=2013 |issue=9 |article-number=12 |doi=10.1007/JHEP09(2013)012 |arxiv=1210.6996 |bibcode=2013JHEP...09..012A }}</ref> The theory of [[loop quantum gravity]] proposes that the curvature and density at the center of a black hole is large, but not infinite.<ref>{{Cite journal |last1=Bojowald |first1=Martin |title=Black-Hole Models in Loop Quantum Gravity |journal=Universe |date=2020 |volume=6 |issue=8 |page=125 |doi=10.3390/universe6080125 |arxiv=2009.13565 |bibcode=2020Univ....6..125B |doi-access=free }}</ref>

== Formation ==
Black holes are formed by [[gravitational collapse]] of massive stars, either by direct collapse or during a supernova explosion in a process called "fallback".<ref>{{Cite journal |last1=Woosley |first1=S. E. |last2=Heger |first2=A. |last3=Weaver |first3=T. A. |date=7 November 2002 |title=The evolution and explosion of massive stars |url=https://link.aps.org/doi/10.1103/RevModPhys.74.1015 |journal=Reviews of Modern Physics |language=en |volume=74 |issue=4 |pages=1015–1071 |doi=10.1103/RevModPhys.74.1015 |bibcode=2002RvMP...74.1015W |issn=0034-6861|url-access=subscription }}</ref> Black holes can result from the merger of two [[neutron star]]s or a neutron star and a black hole.<ref>{{Cite journal |last1=Zappa |first1=Francesco |last2=Bernuzzi |first2=Sebastiano |last3=Pannarale |first3=Francesco |last4=Mapelli |first4=Michela |last5=Giacobbo |first5=Nicola |date=25 July 2019 |title=Black-Hole Remnants from Black-Hole–Neutron-Star Mergers |url=https://link.aps.org/doi/10.1103/PhysRevLett.123.041102 |journal=Physical Review Letters |language=en |volume=123 |issue=4 |article-number=041102 |doi=10.1103/PhysRevLett.123.041102 |pmid=31491270 |arxiv=1903.11622 |bibcode=2019PhRvL.123d1102Z |issn=0031-9007}}</ref> Other more speculative mechanisms include [[primordial black hole]]s created from density fluctuations in the early universe, the collapse of [[Dark star (Newtonian mechanics)|dark star]]s, a hypothetical object powered by annihilation of [[dark matter]], or from hypothetical self-interacting dark matter.<ref>{{Cite journal |last1=Inayoshi |first1=Kohei |last2=Visbal |first2=Eli |last3=Haiman |first3=Zoltán |date=18 August 2020 |title=The Assembly of the First Massive Black Holes |url=https://www.annualreviews.org/content/journals/10.1146/annurev-astro-120419-014455 |journal=Annual Review of Astronomy and Astrophysics |language=en |volume=58 |issue=<!--none--> |pages=27–97 |doi=10.1146/annurev-astro-120419-014455 |arxiv=1911.05791 |bibcode=2020ARA&A..58...27I |issn=0066-4146}}</ref>

=== Gravitational collapse ===
{{main|Gravitational collapse}}
[[File:Images of gas cloud being ripped apart by the black hole at the centre of the Milky Way ESO.jpg|thumb|Gas cloud being ripped apart by black hole at the centre of the Milky Way (observations from 2006, 2010 and 2013 are shown in blue, green and red, respectively)<ref>{{cite press release |title=Ripped Apart by a Black Hole |url=http://www.eso.org/public/news/eso1332/ |access-date=19 July 2013 |work=ESO |date=17 July 2013 |archive-url=https://web.archive.org/web/20130721014626/http://www.eso.org/public/news/eso1332/ |archive-date=21 July 2013 }}</ref>]]

Gravitational collapse occurs when an object's internal [[pressure]] is insufficient to resist the object's own gravity. At the end of a star's life, it will run out of [[hydrogen]] to [[nuclear fusion|fuse]], and will start fusing more and more massive elements, until it gets to [[iron]]. Since the fusion of any heavier elements would [[endothermic reaction|require more energy than they would release]], the star can no longer perform nuclear fusion. If the iron core of the star is too massive, the star will no longer be able to support itself and will undergo gravitational collapse.<ref>{{Cite journal |last1=Janka |first1=H. |last2=Langanke |first2=K. |last3=Marek |first3=A. |last4=Martinezpinedo |first4=G. |last5=Muller |first5=B. |title=Theory of core-collapse supernovae |journal=Physics Reports |date=2007 |volume=442 |issue=1–6 |pages=38–74 |doi=10.1016/j.physrep.2007.02.002 |arxiv=astro-ph/0612072 |bibcode=2007PhR...442...38J }}</ref><ref>{{Cite journal |last1=Fryer |first1=Chris L. |last2=Holz |first2=Daniel E. |last3=Hughes |first3=Scott A. |title=Gravitational Wave Emission from Core Collapse of Massive Stars |journal=The Astrophysical Journal |date=2002 |volume=565 |issue=1 |pages=430–446 |doi=10.1086/324034 |arxiv=astro-ph/0106113 |bibcode=2002ApJ...565..430F }}</ref>

The collapse may be stopped by the [[Degenerate matter|degeneracy pressure]] of the star's constituents, allowing the condensation of matter into an exotic [[Degenerate matter|denser state]]. Degeneracy pressure occurs from the [[Pauli exclusion principle]]—Particles will resist being in the same place as each other. Smaller progenitor stars, with masses less than about {{Solar mass|8}}, will be held together by the degeneracy pressure of electrons and will become a [[white dwarf]]. For more massive progenitor stars, electron degeneracy pressure is no longer strong enough to resist the force of gravity and the star will be held together by [[neutron degeneracy pressure]], which can occur at much higher densities, forming a [[neutron star]]. If the star is still too massive, even neutron degeneracy pressure will not be able to resist the force of gravity and the star will collapse into a black hole.<ref>{{Cite journal |last1=Bennett |first1=Jeffrey |title=Degeneracy pressure in stars and stellar corpses |journal=The Physics Teacher |date=2025 |volume=63 |issue=3 |pages=212–213 |doi=10.1119/5.0260882 |bibcode=2025PhTea..63c.212B }}</ref><ref name="Carroll5.8" /> Which type forms depends on the mass of the remnant of the original star left if the outer layers have been blown away (for example, in a [[Type II supernova]]). The mass of the remnant, the collapsed object that survives the explosion, can be substantially less than that of the original star. Remnants exceeding {{Solar mass|5}} are produced by stars that were over {{Solar mass|20}} before the collapse.<ref name="Carroll5.8">{{harvnb|Carroll|2004|loc=Section 5.8}}</ref>

The gravitational collapse of heavy stars is assumed to be responsible for the formation of [[stellar mass black hole]]s. [[Star formation]] in the early universe may have resulted in very massive stars, which upon their collapse would have produced black holes of up to {{Solar mass|{{10^|3}}}}. These black holes could be the seeds of the supermassive black holes found in the centres of most galaxies.<ref name="ReesVolonteri">{{cite conference |first1=M. J. |series=Proceedings of the International Astronomical Union |last1=Rees |first2=M. |last2=Volonteri |author2-link=Marta Volonteri|title=Massive black holes: Formation and evolution |editor1-first=V. |editor1-last=Karas |editor2-first=G. |editor2-last=Matt |book-title=Black Holes from Stars to Galaxies – Across the Range of Masses |pages=51–58 |date=2007 |isbn=978-0-521-86347-6 |arxiv=astro-ph/0701512 |bibcode=2007IAUS..238...51R |doi=10.1017/S1743921307004681 |doi-access=free |s2cid=14844338 }}</ref> It has further been suggested that massive black holes with typical masses of ~{{Solar mass|{{10^|5}}}} could have formed from the direct collapse of gas clouds in the young universe.<ref name="pacucci2016">{{cite journal |last1=Pacucci |first1=F. |last2=Ferrara |first2=A. |last3=Grazian |first3=A. |last4=Fiore |first4=F. |last5=Giallongo |first5=E. |title=First Identification of Direct Collapse Black Hole Candidates in the Early Universe in CANDELS/GOODS-S |journal=Mon. Not. R. Astron. Soc. |volume=459 |issue=2 |year=2016 |page=1432 |doi=10.1093/mnras/stw725 |doi-access=free |arxiv=1603.08522 |bibcode=2016MNRAS.459.1432P|s2cid=118578313 }}</ref> These massive objects have been proposed as the seeds that eventually formed the earliest quasars observed already at redshift <math>z \sim 7</math>.<ref>{{cite journal|last1=Bañados|first1=Eduardo|last2=Venemans|first2=Bram P.|last3=Mazzucchelli|first3=Chiara|last4=Farina|first4=Emanuele P.|last5=Walter|first5=Fabian |last6=Wang|first6=Feige |last7=Decarli|first7=Roberto |last8=Stern|first8=Daniel |last9=Fan|first9=Xiaohui |last10=Davies|first10=Frederick B. |last11=Hennawi|first11=Joseph F. |date=1 January 2018|title=An 800-million-solar-mass black hole in a significantly neutral Universe at a redshift of 7.5|journal=Nature|volume=553|issue=7689|pages=473–476|doi=10.1038/nature25180|pmid=29211709|arxiv=1712.01860|bibcode=2018Natur.553..473B|s2cid=205263326}}</ref> Some candidates for such objects have been found in observations of the young universe.<ref name="pacucci2016" />

While most of the energy released during gravitational collapse is emitted very quickly, an outside observer does not actually see the end of this process. Even though the collapse takes a finite amount of time from the [[frame of reference|reference frame]] of infalling matter, a distant observer would see the infalling material slow and halt just above the event horizon, due to gravitational time dilation. Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms delayed an infinite amount of time. Thus the external observer never sees the formation of the event horizon; instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away.<ref>{{cite journal |last1=Penrose |first1=R. |author-link1=Roger Penrose |title=Gravitational Collapse: The Role of General Relativity |journal=General Relativity and Gravitation |volume=34 |issue=7 |page=1141 |date=2002 |doi=10.1023/A:1016578408204 |url=http://www.imamu.edu.sa/Scientific_selections/abstracts/Physics/Gravitational%20Collapse%20The%20Role%20of%20General.pdf |bibcode=2002GReGr..34.1141P |s2cid=117459073|archive-url=https://web.archive.org/web/20130526224126/http://www.imamu.edu.sa/Scientific_selections/abstracts/Physics/Gravitational%20Collapse%20The%20Role%20of%20General.pdf |archive-date=26 May 2013 }}</ref>

==== Primordial black holes and the Big Bang ====
Gravitational collapse requires great density.{{Dubious |reason=SMBHs aren't necessary dense.|date=October 2025}} In the current epoch of the universe these high densities are found only in stars, but in the early universe shortly after the Big Bang densities were much greater, possibly allowing for the creation of black holes. High density alone is not enough to allow black hole formation since a uniform mass distribution will not allow the mass to bunch up. In order for [[primordial black holes]] to have formed in such a dense medium, there must have been initial density perturbations{{Definition needed|date=October 2025}} that could then grow under their own gravity. Different models for the early universe vary widely in their predictions of the scale of these fluctuations. Various models predict the creation of primordial black holes ranging in size from a [[Planck mass]] (<math> m_P = \sqrt{\hbar c/G} </math> ≈ {{val|1.2|e=19|ul=GeV/c2}} ≈ {{val|2.2|e=-8|u=kg}}) to hundreds of thousands of solar masses.<ref name="carr primordial">{{cite book |last1=Carr |first1=B. J. |chapter=Primordial Black Holes: Do They Exist and Are They Useful? |editor1-first=H. |editor1-last=Suzuki |editor2-first=J. |editor2-last=Yokoyama |editor3-first=Y. |editor3-last=Suto |editor4-first=K. |editor4-last=Sato |title=First identification of direct collapse black hole candidates in the early Universe in CANDELS/GOODS-S |journal=Monthly Notices of the Royal Astronomical Society |pages=astro–ph/0511743 |publisher=Universal Academy Press |date=2005 |volume=459 |issue=2 |doi=10.1093/mnras/stw725 |doi-access=free |isbn=978-4-946443-94-7 |arxiv=astro-ph/0511743 |bibcode=2005astro.ph.11743C}}</ref>

Despite the early universe being extremely [[density|dense]], it did not re-collapse into a black hole during the Big Bang, since the expansion rate was greater than the attraction. Following [[inflation theory]],{{clarify|date=October 2025}} general relativity predicts that the gravitational field slows the expansion of the universe.The negative pressure overcomes the positive energy density to produce a net repulsive gravitational field.<ref>{{cite web |last=Guth |first=Alan |date=1997 |title=Was Cosmic Inflation the 'Bang' of the Big Bang? - A. Guth |url=https://ned.ipac.caltech.edu/level5/Guth/Guth3.html |access-date=2 July 2025 |website=NASA/IPAC Extragalactic Database (NED)}}</ref>{{Explain|date=October 2025}}

Models for the gravitational collapse of objects of relatively constant size, such as [[star]]s, do not necessarily apply in the same way to rapidly expanding space such as the Big Bang.<ref>{{cite web |author1=Philip Gibbs |title=Is the Big Bang a black hole? |url=http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html |publisher=[[John Baez]] |access-date=16 March 2018 |archive-date=31 December 2018 |archive-url=https://web.archive.org/web/20181231021714/http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html |url-status=live }}</ref>

=== High-energy collisions ===
In principle, black holes could be formed in [[high-energy physics|high-energy]] particle collisions that achieve sufficient density. As of 2002, no such events have been detected, either directly or indirectly as a deficiency of the mass balance in [[particle accelerator]] experiments.<ref>{{Cite journal |last1=Giddings |first1=S. B. |last2=Thomas |first2=S. |title=High energy colliders as black hole factories: The end of short distance physics |date=2002 |journal=Physical Review D |volume=65 |issue=5 |article-number=056010 |doi=10.1103/PhysRevD.65.056010 |arxiv=hep-ph/0106219|bibcode=2002PhRvD..65e6010G|s2cid=1203487 }}</ref>
Hypothetical [[micro black hole]]s created in the high-energy collisions that occur when [[cosmic ray]]s hit the Earth's atmosphere, or possibly in the [[Large Hadron Collider]] at [[CERN]], would not be able to aggregate additional mass.<ref name="LHCsafety">{{cite journal |url=http://lsag.web.cern.ch/lsag/LSAG-Report.pdf |title=Review of the Safety of LHC Collisions |journal=Journal of Physics G: Nuclear Physics |volume=35 |issue=11 |article-number=115004 |author=LHC Safety Assessment Group |url-status=live |archive-url=https://web.archive.org/web/20100414160742/http://lsag.web.cern.ch/lsag/LSAG-Report.pdf |archive-date=14 April 2010 |bibcode=2008JPhG...35k5004E |year=2008 |arxiv=0806.3414 |doi=10.1088/0954-3899/35/11/115004|s2cid=53370175 }}</ref> Even if micro black holes could be formed, it is expected that they would [[black hole evaporation|evaporate]] in about 10{{sup|−25}} seconds, posing no threat to the Earth.<ref>{{cite journal |last=Cavaglià |first=M. |title=Particle accelerators as black hole factories? |journal=Einstein-Online |volume=4 |page=1010 |date=2010 |url=http://www.einstein-online.info/spotlights/accelerators_bh/|archive-url=https://web.archive.org/web/20130508085759/http://www.einstein-online.info/spotlights/accelerators_bh |archive-date=8 May 2013 |access-date=8 May 2013}}</ref>

== Evolution ==
=== Growth ===
[[File:BBH gravitational lensing of gw150914.webm|alt=A simulation of two black holes colliding to form a super massive black hole|thumb|Simulation of two black holes colliding]]

Once a black hole has formed, it can continue to grow by absorbing additional [[matter]]. Any black hole will continually absorb gas and [[interstellar dust]] from its surroundings. This growth process is one possible way through which some supermassive black holes may have been formed, although the [[Supermassive black hole#Formation|formation of supermassive black holes]] is still an open field of research.<ref name="ReesVolonteri" /> A similar process has been suggested for the formation of [[intermediate-mass black hole]]s found in [[globular cluster]]s.<ref>{{cite journal |first1=E. |last1=Vesperini |first2=S. L. W. |last2=McMillan |first3=A. |last3=d'Ercole |first4=F. |last4=d'Antona |display-authors=3 |title=Intermediate-Mass Black Holes in Early Globular Clusters |journal=The Astrophysical Journal Letters |volume=713 |issue=1 |pages=L41–L44 |date=2010 |doi=10.1088/2041-8205/713/1/L41 |arxiv=1003.3470 |bibcode=2010ApJ...713L..41V |s2cid=119120429}}</ref> Black holes can also merge with other objects such as stars or even other black holes. This is thought to have been important, especially in the early growth of supermassive black holes, which could have formed from the aggregation of many smaller objects.<ref name="ReesVolonteri" /> The process has also been proposed as the origin of some intermediate-mass black holes.<ref>{{cite journal |last1=Zwart |first1=S. F. P. |last2=Baumgardt |first2=H. |last3=Hut |first3=P. |last4=Makino |first4=J. |last5=McMillan |first5=S. L. W. |display-authors=3 |title=Formation of massive black holes through runaway collisions in dense young star clusters |journal=Nature |volume=428 |issue=6984 |date=2004 |doi=10.1038/nature02448 |pmid=15085124 |arxiv=astro-ph/0402622 |bibcode=2004Natur.428..724P |pages=724–726 |s2cid=4408378}}</ref><ref>{{cite journal |last1=O'Leary |first1=R. M. |last2=Rasio |first2=F. A. |last3=Fregeau |first3=J. M. |last4=Ivanova |first4=N. |last5=o'Shaughnessy |first5=R. |display-authors=3 |title=Binary Mergers and Growth of Black Holes in Dense Star Clusters |journal=The Astrophysical Journal |volume=637 |issue=2 |pages=937–951 |date=2006 |doi=10.1086/498446 |arxiv=astro-ph/0508224 |bibcode=2006ApJ...637..937O |s2cid=1509957}}</ref>

=== Evaporation ===
{{main|Hawking radiation}}

In 1974, Hawking predicted that black holes are not entirely black but emit small amounts of thermal radiation at a temperature ''ħc''{{sup|3}}/(8''πGM''[[Boltzmann constant|''k''{{sub|B}}]]);<ref name=Hawking1974>{{cite journal |last=Hawking |first=S. W. |author-link1=Stephen Hawking |title=Black hole explosions? |journal=Nature |date=1974 |volume=248 |issue=5443 |pages=30–31 |doi=10.1038/248030a0|bibcode=1974Natur.248...30H|s2cid=4290107 }}</ref> this effect has become known as Hawking radiation. By applying quantum field theory to a static black hole background, he determined that a black hole should emit particles that display a perfect [[black body spectrum]]. Since Hawking's publication, many others have verified the result through various approaches.<ref>{{cite journal |last=Page |first=D. N. |title=Hawking radiation and black hole thermodynamics |journal=New Journal of Physics |volume=7 |issue=1 |page=203 |date=2005 |arxiv=hep-th/0409024 |doi=10.1088/1367-2630/7/1/203|bibcode=2005NJPh....7..203P|s2cid=119047329 }}</ref> If Hawking's theory of black hole radiation is correct, then black holes are expected to shrink and evaporate over time as they lose mass by the emission of photons and other particles.<ref name=Hawking1974 /> The temperature of this thermal spectrum ([[Hawking temperature]]) is proportional to the surface gravity of the black hole, which, for a Schwarzschild black hole, is inversely proportional to the mass. Hence, large black holes emit less radiation than small black holes.<ref>{{harvnb|Carroll|2004|loc=Ch. 9.6}}</ref>

A stellar black hole of {{Solar mass|1}} has a Hawking temperature of 62&nbsp;[[nanokelvin]]s.<ref>{{cite news |last1=Siegel |first1=Ethan |author-link1=Ethan Siegel |title=Ask Ethan: Do Black Holes Grow Faster Than They Evaporate? |url=https://www.forbes.com/sites/startswithabang/2017/08/19/ask-ethan-do-black-holes-grow-faster-than-they-evaporate/ |access-date=17 March 2018 |work=Forbes ("Starts With A Bang" blog) |date=2017 |archive-date=22 November 2018 |archive-url=https://web.archive.org/web/20181122031830/https://www.forbes.com/sites/startswithabang/2017/08/19/ask-ethan-do-black-holes-grow-faster-than-they-evaporate/ |url-status=live }}</ref> This is far less than the 2.7&nbsp;K temperature of the [[cosmic microwave background]] radiation. Stellar-mass or larger black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and thus will grow instead of shrinking.<ref>{{cite journal |last1=Sivaram |first1=C. |title=Black hole Hawking radiation may never be observed! |journal=General Relativity and Gravitation |date=2001 |volume=33 |issue=2 |pages=175–181 |bibcode=2001GReGr..33..175S |doi=10.1023/A:1002753400430|s2cid=118913634 }}</ref> To have a Hawking temperature larger than 2.7&nbsp;K (and be able to evaporate), a black hole would need a mass less than the [[Moon]]. Such a black hole would have a diameter of less than a tenth of a millimetre.<ref>{{cite web |url=http://www.einstein-online.info/elementary/quantum/evaporating_bh/?set_language=en |title=Evaporating black holes? |website=Einstein online |publisher=Max Planck Institute for Gravitational Physics |date=2010 |access-date=12 December 2010 |archive-url=https://web.archive.org/web/20110722055345/http://www.einstein-online.info/elementary/quantum/evaporating_bh/?set_language=en |archive-date=22 July 2011}}</ref>

If a black hole is very small, the radiation effects are expected to become very strong. A black hole with the mass of a car would have a diameter of about 10{{sup|−24}}&nbsp;m and take a nanosecond to evaporate, during which time it would briefly have a luminosity of more than 200 times that of the Sun. Lower-mass black holes are expected to evaporate even faster; for example, a black hole of mass 1&nbsp;TeV/''c''{{sup|2}} would take less than 10{{sup|−88}} seconds to evaporate completely.{{Explain|date=October 2025}} For such a small black hole, quantum gravity effects are expected to play an important role and could hypothetically make such a small black hole stable, although current developments in quantum gravity do not indicate this is the case.<ref>{{cite journal |last1=Giddings |first1=S. B. |last2=Mangano |first2=M. L. |title=Astrophysical implications of hypothetical stable TeV-scale black holes |journal=Physical Review D |volume=78 |issue=3 |article-number=035009 |date=2008 |doi=10.1103/PhysRevD.78.035009 |arxiv=0806.3381 |bibcode=2008PhRvD..78c5009G |s2cid=17240525}}</ref><ref>{{cite journal |last1=Peskin |first1=M. E. |title=The end of the world at the Large Hadron Collider? |journal=Physics |volume=1 |article-number=14 |date=2008 |doi=10.1103/Physics.1.14 |bibcode=2008PhyOJ...1...14P|doi-access=free}}</ref>

The Hawking radiation for an astrophysical black hole is predicted to be very weak and would thus be exceedingly difficult to detect from Earth. A possible exception is the burst of gamma rays emitted in the last stage of the evaporation of primordial black holes. Searches for such flashes have proven unsuccessful and provide stringent limits on the possibility of existence of low mass primordial black holes.<ref>{{cite journal |last1=Fichtel |first1=C. E. |last2=Bertsch |first2=D. L. |last3=Dingus |first3=B. L.|author3-link= Brenda Dingus |last4=Esposito |first4=J. A. |last5=Hartman |first5=R. C. |last6=Hunter |first6=S. D. |last7=Kanbach |first7=G. |last8=Kniffen |first8=D. A. |last9=Lin |first9=Y. C. |display-authors=3 |title=Search of the energetic gamma-ray experiment telescope (EGRET) data for high-energy gamma-ray microsecond bursts |journal=Astrophysical Journal |volume=434 |issue=2 |pages=557–559 |date=1994 |doi=10.1086/174758|bibcode=1994ApJ...434..557F |last10=Mattox |first10=J. R. |last11=Mayer-Hasselwander |first11=H. A. |last12=McDonald |first12=L. |last13=Michelson |first13=P. F. |last14=Von Montigny |first14=C. |last15=Nolan |first15=P. L. |last16=Schneid |first16=E. J. |last17=Sreekumar |first17=P. |last18=Thompson |first18=D. J.}}</ref>{{By how much|date=October 2025}} NASA's [[Fermi Gamma-ray Space Telescope]] launched in 2008 will continue the search for these flashes.<ref>{{cite web |first=R. |last=Naeye |title=Testing Fundamental Physics |url=http://www.nasa.gov/mission_pages/GLAST/science/testing_fundamental_physics.html |publisher=NASA |access-date=16 September 2008 |url-status=live |archive-url=https://web.archive.org/web/20080831045232/http://www.nasa.gov/mission_pages/GLAST/science/testing_fundamental_physics.html |archive-date=31 August 2008}}</ref>{{Update inline|date=October 2025}}

If black holes evaporate via Hawking radiation, a solar mass black hole will evaporate (beginning once the temperature of the cosmic microwave background drops below that of the black hole) over a period of 10{{sup|64}} years.<ref name="Frautschi1982" /> A supermassive black hole with a mass of {{Solar mass|{{10^|11}}}} will evaporate in around 2×10{{sup|100}} years.<ref name=page>{{cite journal | doi = 10.1103/PhysRevD.13.198 | volume=13 | title=Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole | year=1976 | journal=Physical Review D | pages=198–206 | last1 = Page | first1 = Don N.| issue=2 | bibcode=1976PhRvD..13..198P}}. See in particular equation (27).</ref> During the collapse of a supercluster of galaxies, supermassive black holes are predicted to grow to up to {{solar mass|{{10^|14}}}}. Even these would evaporate over a [[Chronology of the universe|timescale]] of up to 10{{sup|106}} years.<ref name="Frautschi1982">{{cite journal |last1=Frautschi |first1=S. |title=Entropy in an Expanding Universe |journal=Science |volume=217 |issue=4560 |year=1982 |pages=593–599 |doi=10.1126/science.217.4560.593 |pmid=17817517 |bibcode=1982Sci...217..593F|s2cid=27717447 }} See page 596: table{{nbsp}}1 and section "black hole decay" and previous sentence on that page.</ref>

== Observational evidence ==
Millions of black holes with around 30 solar masses derived from stellar collapse are expected to exist in the Milky Way. Even a [[dwarf galaxy]] like [[Draco (dwarf galaxy)|Draco]] should have hundreds.<ref>{{Cite journal |last1=Elbert |first1=Oliver D. |last2=Bullock |first2=James S. |last3=Kaplinghat |first3=Manoj |date=1 January 2018 |title=Counting black holes: The cosmic stellar remnant population and implications for LIGO |url=https://academic.oup.com/mnras/article/473/1/1186/4060726 |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=473 |issue=1 |pages=1186–1194 |doi=10.1093/mnras/stx1959 |doi-access=free |issn=0035-8711|arxiv=1703.02551 }}</ref> Only a few of these have been detected.
By nature, black holes do not themselves emit any electromagnetic radiation other than the hypothetical Hawking radiation, so astrophysicists searching for black holes must generally rely on indirect observations.

=== Direct interferometry ===
[[File:A_view_of_the_M87_supermassive_black_hole_in_polarised_light.tif|thumb|A view of supermassive black hole [[M87*]] in polarised light]]
[[File:EHT_Saggitarius_A_black_hole.tif|thumb|[[Sagittarius A*]], the supermassive black hole in the center of the Milky Way]]

The [[Event Horizon Telescope]] (EHT) is an active program that directly observes the immediate environment of black holes' event horizons, such as the black hole at the centre of the Milky Way. In April 2017, EHT began observing the black hole at the centre of [[Messier 87]].<ref name="eht">{{cite web |url=https://eventhorizontelescope.org/galleries/2017-observations |title=April 2017 Observations |work=Event Horizon Telescope |access-date=11 April 2019 |archive-date=10 April 2019 |archive-url=https://web.archive.org/web/20190410223148/https://eventhorizontelescope.org/galleries/2017-observations |url-status=live }}</ref><ref name="NYT-20240124">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=That Famous Black Hole Gets a Second Look - Repeated studies of the supermassive black hole in the galaxy Messier 87 confirm that it continues to act as Einstein's theory predicted it would. |url=https://www.nytimes.com/2024/01/24/science/space/black-holes-photography-m87.html |date=24 January 2024 |work=[[The New York Times]] |url-status=live |archive-url=https://archive.today/20240124200523/https://www.nytimes.com/2024/01/24/science/space/black-holes-photography-m87.html |archive-date=24 January 2024 |access-date=25 January 2024 }}</ref> "In all, eight radio observatories on six mountains and four continents observed the galaxy in Virgo on and off for 10 days in April 2017" to provide the data yielding the image in April 2019.<ref name=OverbyeApril2019>{{cite news |url=https://www.nytimes.com/2019/04/10/science/black-hole-picture.html |title=Darkness Visible, Finally: Astronomers Capture First Ever Image of a Black Hole |last=Overbye |first=Dennis |date=10 April 2019 |access-date=11 April 2019 |newspaper=The New York Times |archive-date=21 May 2019 |archive-url=https://web.archive.org/web/20190521020231/https://www.nytimes.com/2019/04/10/science/black-hole-picture.html |url-status=live }}</ref>{{Whose quote}}

After two years of data processing, EHT released its first  image of a black hole, at the center of the Messier 87 galaxy.<ref>{{cite news |url=https://www.nytimes.com/video/science/space/100000006453594/first-image-black-hole.html |type=video |date=10 April 2019 |agency=AP |newspaper=The New York Times |title=Astronomers Reveal the First Picture of a Black Hole |access-date=11 April 2019 |archive-date=22 May 2019 |archive-url=https://web.archive.org/web/20190522052307/https://www.nytimes.com/video/science/space/100000006453594/first-image-black-hole.html |url-status=live }}</ref><ref>{{cite web |last=Doeleman |first=Shep |title=The Event Horizon Telescope: Imaging and Time-Resolving a Black Hole |url=https://www.youtube.com/watch?v=_yGSgUUYDQ8&t=46m50s |website=Physics @ Berkeley |date=4 April 2016 |time=46:50 |access-date=8 July 2016 |url-status=live |archive-url=https://web.archive.org/web/20161201115303/https://www.youtube.com/watch?v=_yGSgUUYDQ8&t=46m50s |archive-date=1 December 2016}}</ref> What is visible is not the black hole—which shows as black because of the loss of all light within this dark region. Instead, it is the accretion disk bordering the event horizon, depicted in the image as orange or red, that define the black hole.<ref name="GrossmanApril2019">{{cite news |last1=Grossman |first1=Lisa |last2=Conover |first2=Emily |author-link2=Emily Conover |date=10 April 2019 |title=The first picture of a black hole opens a new era of astrophysics |url=https://www.sciencenews.org/article/black-hole-first-picture-event-horizon-telescope |url-status=live |archive-url=https://web.archive.org/web/20190427192956/https://www.sciencenews.org/article/black-hole-first-picture-event-horizon-telescope |archive-date=27 April 2019 |access-date=11 April 2019 |newspaper=Science News}}</ref>

On 12 May 2022, the EHT released the first image of [[Sagittarius A*]], the supermassive black hole at the centre of the Milky Way galaxy. The published image displayed the same ring-like structure and "shadow" seen in the M87* black hole. The boundary of the shadow or area of less brightness matches the predicted gravitationally lensed photon orbits.<ref>{{cite journal |last1=Event Horizon Telescope Collaboration |last2=Akiyama |first2=Kazunori |last3=Alberdi |first3=Antxon |last4=Alef |first4=Walter |last5=Algaba |first5=Juan Carlos |last6=Anantua |first6=Richard |last7=Asada |first7=Keiichi |last8=Azulay |first8=Rebecca |last9=Bach |first9=Uwe |last10=Baczko |first10=Anne-Kathrin |last11=Ball |first11=David |last12=Baloković |first12=Mislav |last13=Barrett |first13=John |last14=Bauböck |first14=Michi |last15=Benson |first15=Bradford A. |date=1 May 2022 |title=First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way |journal=The Astrophysical Journal Letters |volume=930 |issue=2 |quote=The ring usually lies near the gravitationally lensed photon orbits that define the boundary of what we hereafter refer to as the black hole "shadow." |pages=L12 |doi=10.3847/2041-8213/ac6674 |doi-access=free |bibcode=2022ApJ...930L..12E |issn=2041-8205|arxiv=2311.08680 }}</ref>{{Explain|date=October 2025}} The image was created using the same techniques as for the M87 black hole. The imaging process for Sagittarius A*, which is more than a thousand times less massive than M87*, was significantly more complex because of the instability of its surroundings.<ref>{{CC-notice|by4}} {{cite web |title=Astronomers Reveal First Image of the Black Hole at the Heart of Our Galaxy |url=https://eventhorizontelescope.org/blog/astronomers-reveal-first-image-black-hole-heart-our-galaxy |access-date=22 June 2022 |website=eventhorizontelescope.org |date=12 May 2022 |language=en}}</ref>{{Clarify|date=October 2025}} The image of Sagittarius A* was partially blurred by turbulent [[Plasma (physics)|plasma]] between it and Earth, an effect which prevents resolution of the image at longer wavelengths.<ref>{{cite journal |last=C. Bower |first=Geoffrey |date=May 2022 |title=Focus on First Sgr A* Results from the Event Horizon Telescope |url=https://iopscience.iop.org/journal/2041-8205/page/Focus_on_First_Sgr_A_Results |journal= The Astrophysical Journal Letters  |volume= |issue=2041–8205}}</ref>

The brightening of this material in the bottom half of the processed EHT image is thought to be caused by [[Relativistic beaming|Doppler beaming]], whereby material approaching the viewer at relativistic speeds is perceived as brighter than material moving away. In the case of a black hole, this phenomenon implies that the visible material is rotating at relativistic speeds (>{{convert|1,000|km/s|mph|abbr=on|disp=sqbr}}), the only speeds at which it is possible to centrifugally balance the immense gravitational attraction of the black hole, and thereby remain in orbit above the event horizon.{{Explain|date=October 2025}} This configuration of bright material implies that the EHT observed both [[M87*]] and its disk rotating clockwise.<ref>{{cite journal|last=Event Horizon Telescope Collaboration|title=First M87 Event Horizon Telescope Results. VII. Polarization of the Ring|journal=The Astrophysical Journal|year=2021|volume=910|issue=1|page=L12|doi=10.3847/2041-8213/abe71d|arxiv=2105.01169|bibcode=2021ApJ...910L..12E|s2cid=233851995|doi-access=free }}</ref><ref name=GrossmanApril2019/>{{Clarify|date=October 2025}}

[[File:A view of the jet and shadow of M87’s black hole (eso2305a).jpg|thumb|The M87* black hole and its relativistic jet]]

In 2015, the EHT detected magnetic fields just outside the event horizon of Sagittarius A* and even discerned some of their properties. The field lines that pass through the accretion disc were a complex mixture of ordered and tangled. Theoretical studies of black holes had predicted the existence of magnetic fields.<ref>{{cite journal |title=Resolved magnetic-field structure and variability near the event horizon of Sagittarius A* |journal=Science |date=4 December 2015 |pages=1242–1245 |volume=350 |issue=6265 |doi=10.1126/science.aac7087 |first1=M. D. |last1=Johnson |first2=V. L. |last2=Fish |first3=S. S. |last3=Doeleman |first4=D. P. |last4=Marrone |first5=R. L. |last5=Plambeck |first6=J. F. C. |last6=Wardle |first7=K. |last7=Akiyama |first8=K. |last8=Asada |first9=C. |last9=Beaudoin |arxiv=1512.01220 |bibcode=2015Sci...350.1242J |pmid=26785487|s2cid=21730194 }}</ref><ref>{{cite web |title=Event Horizon Telescope Reveals Magnetic Fields at Milky Way's Central Black Hole |url=https://www.cfa.harvard.edu/news/2015-28 |website=cfa.harvard.edu |access-date=12 January 2016 |date=3 December 2015 |url-status=live |archive-url=https://web.archive.org/web/20151231211408/https://www.cfa.harvard.edu/news/2015-28 |archive-date=31 December 2015}}</ref>

In April 2023, an image of the shadow of the Messier 87 black hole and the related high-energy jet, viewed together for the first time, was presented.<ref name="NYT-20230426">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=A Fresh View of an Increasingly Familiar Black Hole - Radio astronomers have captured a wide-angle image of one of the most violent locales in the cosmos. |url=https://www.nytimes.com/2023/04/26/science/astronomy-black-hole-m87.html |date=26 April 2023 |work=[[The New York Times]] |url-status=live |archive-url=https://archive.today/20230426212932/https://www.nytimes.com/2023/04/26/science/astronomy-black-hole-m87.html  |archive-date=26 April 2023 |access-date=26 April 2023 }}</ref><ref name="NAT-20230426">{{cite journal |author=Lu, Ru-Sen |display-authors=et al |title=A ring-like accretion structure in M87 connecting its black hole and jet |date=26 April 2023 |journal=[[Nature (journal)|Nature]] |volume=616 |issue=7958 |pages=686–690 |doi=10.1038/s41586-023-05843-w |pmid=37100940 |pmc=10132962 |arxiv=2304.13252 |bibcode=2023Natur.616..686L }}</ref>

=== Detection of gravitational waves from merging black holes ===
[[File:LIGO measurement of gravitational waves.svg|thumb|LIGO measurement of the gravitational waves at the Livingston (right) and Hanford (left) detectors, compared with the theoretical predicted values]]

On 14 September 2015, the [[LIGO]] gravitational wave observatory made the first-ever successful [[first observation of gravitational waves|direct observation of gravitational waves]].<ref name="PRL-20160211">{{cite journal |author=Abbott, B.P. |title=Observation of Gravitational Waves from a Binary Black Hole Merger |journal=[[Phys. Rev. Lett.]] |volume=116 |issue=6 |article-number=061102 |year=2016 |doi=10.1103/PhysRevLett.116.061102 |display-authors=etal |arxiv=1602.03837 |bibcode=2016PhRvL.116f1102A |pmid=26918975|s2cid=124959784 }}</ref><ref name="NYT-20160211-db">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=Physicists Detect Gravitational Waves, Proving Einstein Right |url=https://www.nytimes.com/2016/02/12/science/ligo-gravitational-waves-black-holes-einstein.html |date=11 February 2016 |work=[[The New York Times]] |access-date=11 February 2016 |url-status=live |archive-url=https://web.archive.org/web/20160211165128/http://www.nytimes.com/2016/02/12/science/ligo-gravitational-waves-black-holes-einstein.html |archive-date=11 February 2016}}</ref> The signal was consistent with theoretical predictions for the gravitational waves produced by the merger of two black holes: one with about 36 solar masses, and the other around 29 solar masses.<ref name="PRL-20160211" /><ref name="Properties">{{cite journal |collaboration=[[LIGO Scientific Collaboration]] & [[Virgo interferometer|Virgo Collaboration]] |last1=Abbott |first1=Benjamin P. |arxiv=1602.03840 |title=Properties of the binary black hole merger GW150914 |journal=Physical Review Letters |volume=116 |issue=24 |article-number=241102 |date=11 February 2016 |bibcode=2016PhRvL.116x1102A |doi=10.1103/PhysRevLett.116.241102 |pmid=27367378|s2cid=217406416 }}</ref> This observation provides the most concrete evidence for the existence of black holes to date. For instance, the gravitational wave signal suggests that the separation of the two objects before the merger was just 350&nbsp;km, or roughly four times the Schwarzschild radius corresponding to the inferred masses. The objects must therefore have been extremely compact, leaving black holes as the most plausible interpretation.<ref name="PRL-20160211" />{{Why|date=October 2025}}

More importantly, the signal observed by LIGO also included the start of the post-merger [[Binary black hole#Ringdown|ringdown]], the signal produced as the newly formed compact object settles down to a stationary state. Arguably, the ringdown is the most direct way of observing a black hole.<ref name="Cardoso2016">{{cite journal |author1=Cardoso, V. |author2=Franzin, E. |author3=Pani, P. |title=Is the gravitational-wave ringdown a probe of the event horizon? |doi=10.1103/PhysRevLett.116.171101 |pmid=27176511 |journal=[[Physical Review Letters]] |arxiv=1602.07309 |year=2016 |volume=116 |issue=17 |article-number=171101 |bibcode=2016PhRvL.116q1101C|s2cid=206273829 }}</ref> From the LIGO signal, it is possible to extract the frequency and damping time of the dominant mode of the ringdown.{{Definition needed|date=October 2025}} From these, it is possible to infer the mass and angular momentum of the final object, which match independent predictions from numerical simulations of the merger.<ref name="tests">{{cite journal |url=https://dcc.ligo.org/P1500213/public |title=Tests of general relativity with GW150914 |collaboration=[[LIGO Scientific Collaboration]] & [[Virgo interferometer|Virgo Collaboration]] |last1=Abbott |first1=Benjamin P. |journal=Physical Review Letters |date=11 February 2016 |volume=116 |issue=22 |article-number=221101 |doi=10.1103/PhysRevLett.116.221101 |pmid=27314708 |arxiv=1602.03841 |bibcode=2016PhRvL.116v1101A |s2cid=217275338 |access-date=12 February 2016 |archive-url=https://web.archive.org/web/20160215165039/https://dcc.ligo.org/P1500213/public |archive-date=15 February 2016 }}</ref> The frequency and decay time of the dominant mode are determined by the geometry of the photon sphere. Hence, observation of this mode confirms the presence of a photon sphere; however, it cannot exclude possible exotic alternatives to black holes that are compact enough to have a photon sphere.<ref name="Cardoso2016"/><ref name="Murk2023">{{cite journal |last=Murk |first=Sebastian |title=Nomen non est omen: Why it is too soon to identify ultra-compact objects as black holes |journal=International Journal of Modern Physics D |year=2023 |volume=32 |issue=14 |pages=2342012–2342235 |article-number=2342012 |doi=10.1142/S0218271823420129 |arxiv=2210.03750 |bibcode=2023IJMPD..3242012M |s2cid=252781040}}</ref>{{Example needed|date=October 2025}}

The observation also provides the first observational evidence for the existence of stellar-mass black hole binaries. Furthermore, it is the first observational evidence of stellar-mass black holes weighing 25 solar masses or more.<ref name="implications">{{cite journal |collaboration=[[LIGO Scientific Collaboration]] & [[Virgo interferometer|Virgo Collaboration]] |title=Astrophysical Implications of the Binary Black Hole Merger GW150914 |doi=10.3847/2041-8205/818/2/L22 |journal=Astrophys. J. Lett. |volume=818 |number=2 |page=L22 |url=https://dcc.ligo.org/P1500262/public |arxiv=1602.03846 |bibcode=2016ApJ...818L..22A |year=2016 |last1=Abbott |first1=B. P. |hdl=1826/11732 |s2cid=209315965 |url-status=live |archive-url=https://web.archive.org/web/20160316053938/https://dcc.ligo.org/P1500262/public |archive-date=16 March 2016 |doi-access=free }}</ref>

Since then, many more [[List of gravitational wave observations|gravitational wave events]] have been observed.<ref name="ligo list">{{cite web|title=Detection of gravitational waves|url=https://www.ligo.org/detections.php|access-date=9 April 2018|publisher=[[LIGO]]|archive-date=20 May 2020|archive-url=https://web.archive.org/web/20200520134427/https://www.ligo.org/detections.php|url-status=live}}</ref>

=== Stars orbiting Sagittarius A* ===
{{main|Sagittarius A* cluster}}
[[File:SgrA2021.gif|thumb|Stars moving around Sagittarius A* as seen in 2021]]

The [[proper motion]]s of stars near the centre of our own Milky Way provide strong observational evidence that these stars are orbiting a supermassive black hole.<ref name="Gillessen">{{cite journal |last1=Gillessen |first1=S. |last2=Eisenhauer |first2=F. |last3=Trippe |first3=S. |last4=Alexander |first4=T. |last5=Genzel |first5=R. |last6=Martins |first6=F. |last7=Ott |first7=T. |display-authors=3 |title=Monitoring Stellar Orbits around the Massive Black Hole in the Galactic Center |journal=The Astrophysical Journal |volume=692 |issue=2 |pages=1075–1109 |date=2009 |doi=10.1088/0004-637X/692/2/1075 |arxiv=0810.4674 |bibcode=2009ApJ...692.1075G |s2cid=1431308}}</ref> Since 1995, astronomers have tracked the motions of 90 stars orbiting an invisible object coincident with the radio source Sagittarius A*. By fitting their motions to [[Keplerian orbit]]s, the astronomers were able to infer, in 1998, that a {{solar mass|{{val|2.6e6}}}} object must be contained in a volume with a radius of 0.02 [[light-year]]s to cause the motions of those stars.<ref name="Ghez1998">{{cite journal |last1=Ghez |first1=A. M. |last2=Klein |first2=B. L. |last3=Morris |first3=M. |last4=Becklin |first4=E. E. |display-authors=3 |title=High Proper-Motion Stars in the Vicinity of Sagittarius A*: Evidence for a Supermassive Black Hole at the Center of Our Galaxy |journal=The Astrophysical Journal |volume=509 |issue=2 |pages=678–686 |date=1998 |doi=10.1086/306528 |arxiv=astro-ph/9807210 |bibcode=1998ApJ...509..678G |s2cid=18243528}}</ref>

Since then, one of the stars—called [[S2 (star)|S2]]—has completed a full orbit. From the orbital data, astronomers were able to refine the calculations of the mass to {{Solar mass|{{val|4.3e6}}}} and a radius of less than 0.002 light-years for the object causing the orbital motion of those stars.<ref name="Gillessen" /> The upper limit on the object's size is still too large to test whether it is smaller than its Schwarzschild radius. Nevertheless, these observations strongly suggest that the central object is a supermassive black hole as there are no other plausible scenarios for confining so much invisible mass into such a small volume.<ref name="Ghez1998" /> Additionally, there is some observational evidence that this object might possess an event horizon, a feature unique to black holes.<ref>{{Cite journal |title=The Event Horizon of Sagittarius A* |last1=Broderick |first1=Avery |date=August 2009 |journal=The Astrophysical Journal |doi=10.1088/0004-637X/701/2/1357 |last2=Loeb |first2=Abraham |last3=Narayan |first3=Ramesh |volume=701 |issue=2 |pages=1357–1366 |arxiv=0903.1105 |bibcode=2009ApJ...701.1357B|s2cid=12991878 }}</ref>

In 2020, [[Andrea Ghez]] and [[Reinhard Genzel]] shared one-half of the [[Nobel Prize in Physics]] for their discovery that Sagittarius A* was a supermassive black hole.<ref>{{cite web |title=Press release: The Nobel Prize in Physics 2020 |url=https://www.nobelprize.org/prizes/physics/2020/press-release/ |publisher=Nobel Foundation |access-date=6 October 2020}}</ref><ref>{{cite news |last1=Overbye |first1=Dennis |last2=Taylor |first2=Derrick Bryson |title=Nobel Prize in Physics Awarded to 3 Scientists for Work on Black Holes – The prize was awarded half to Roger Penrose for showing how black holes could form and half to Reinhard Genzel and Andrea Ghez for discovering a supermassive object at the Milky Way's center |url=https://www.nytimes.com/2020/10/06/science/nobel-prize-physics.html |date=6 October 2020 |work=[[The New York Times]] |access-date=6 October 2020 }}</ref>

=== Accretion of matter ===
{{see also|Accretion disk}}
[[File:PIA18467-NuSTAR-Plot-BlackHole-BlursLight-20140812.png|thumb|Blurring of X-rays near a black hole ([[NuSTAR]]; 12 August 2014)<ref name="NASA-20140812">{{cite web |author=<!--Staff writer(s); no by-line.--> |date=12 August 2014 |title=NASA's NuSTAR Sees Rare Blurring of Black Hole Light |url=http://www.jpl.nasa.gov/news/news.php?release=2014-273 |archive-url=https://web.archive.org/web/20140813072002/http://www.jpl.nasa.gov/news/news.php?release=2014-273 |archive-date=13 August 2014 |access-date=12 August 2014 |website=[[NASA]]}}</ref>]]
When a black hole accretes matter, the gas in the inner accretion disk orbits at very high speeds because of its proximity to the black hole. The resulting friction is so significant that it heats the inner disk to temperatures at which it emits vast amounts of electromagnetic radiation (mainly [[X-ray]]s). These bright X-ray sources may be detected by telescopes. By the time the matter of the disk reaches the ISCO it will have given off a significant amount of energy - about 0.057mc<sup>2</sup> for a non-rotating black hole or 0.42mc<sup>2</sup> for a rapidly rotating one. Most of this energy (about 90%) is released in a relatively small area, within about 20 times the black hole's gravitational radius from its centre.<ref name=McClintockRemillard2006 /> In many cases, accretion disks are accompanied by [[relativistic jets]] that are emitted along the poles, which carry away much of the energy. The mechanism for the creation of these jets is currently not well understood, in part due to insufficient data.<ref>{{cite news |title=What powers a black hole's mighty jets? |url=https://www.science.org/content/article/what-powers-black-holes-mighty-jets |access-date=19 March 2018 |work=Science {{!}} AAAS |date=19 November 2014 |archive-date=5 May 2019 |archive-url=https://web.archive.org/web/20190505171217/https://www.sciencemag.org/news/2014/11/what-powers-black-holes-mighty-jets |url-status=live }}</ref>

As such, many of the universe's more energetic phenomena have been attributed to the accretion of matter on black holes. In particular, active galactic nuclei and [[quasar]]s are believed to be the accretion disks of supermassive black holes.<ref name="CMS1999" /> Similarly, X-ray binaries are generally accepted to be [[binary star]] systems in which one of the two stars is a compact object accreting matter from its companion.<ref name="CMS1999" /> It has also been suggested that some [[ultraluminous X-ray source]]s may be the accretion disks of intermediate-mass black holes.<ref>{{cite journal |last1=Winter |first1=L. M. |last2=Mushotzky |first2=R. F. |last3=Reynolds |first3=C. S. |title=XMM-Newton Archival Study of the Ultraluminous X-Ray Population in Nearby Galaxies |date=2006 |journal=The Astrophysical Journal |volume=649 |issue=2 |pages=730–752 |arxiv=astro-ph/0512480 |doi=10.1086/506579|bibcode=2006ApJ...649..730W|s2cid=118445260 }}</ref>

Stars have been observed to get torn apart by tidal forces in the immediate vicinity of supermassive black holes in galaxy nuclei, in what is known as a  [[tidal disruption event|tidal disruption event (TDE)]]. Some of the material from the disrupted star forms an accretion disk around the black hole, which emits observable electromagnetic radiation.{{Citation needed|date=October 2025}}

In November 2011, the first direct observation of a quasar accretion disk around a supermassive black hole was reported.<ref>{{cite web |url=https://www.spacetelescope.org/news/heic1116/ |title=Hubble directly observes the disk around a black hole |last=information@eso.org |website=www.spacetelescope.org |access-date=7 March 2016 |url-status=live |archive-url=https://web.archive.org/web/20160308001224/http://spacetelescope.org/news/heic1116/ |archive-date=8 March 2016}}</ref><ref>{{cite journal |last1=Muñoz |first1=José A. |last2=Mediavilla |first2=Evencio |last3=Kochanek |first3=Christopher S. |last4=Falco |first4=Emilio |last5=Mosquera |first5=Ana María |date=1 December 2011 |title=A Study of Gravitational Lens Chromaticity with the Hubble Space Telescope |journal=The Astrophysical Journal |volume=742 |issue=2 |page=67 |doi=10.1088/0004-637X/742/2/67 |arxiv=1107.5932 |bibcode=2011ApJ...742...67M|s2cid=119119359 }}</ref>{{Explain|date=October 2025}}

=== X-ray binaries ===
{{see also|X-ray binary}}
[[File:Chandra image of Cygnus X-1.jpg|thumb|A [[Chandra X-Ray Observatory]] image of [[Cygnus X-1]], which was the first strong black hole candidate discovered]]

[[X-ray binaries]] are binary star systems that emit a majority of their radiation in the [[X-ray]] part of the spectrum. These X-ray emissions cannot derive from an ordinary star and are generally thought to result when compact object accretes matter from a ordinary star. The presence of an ordinary star in such a system provides an opportunity for studying the central object and to determine if it might be a black hole. By studying [[Doppler shift]]s in the spectrum of the companion star it is often possible to obtain the orbital parameters of the system and to obtain an estimate for the mass of the compact object. If this is much larger than the Tolman–Oppenheimer–Volkoff limit (the maximum mass a star can have without collapsing) then the object cannot be a neutron star and is generally expected to be a black hole.<ref name="CMS1999">{{Cite journal |last1=Celotti |first1=A. |last2=Miller |first2=J. C. |last3=Sciama |first3=D. W. |title=Astrophysical evidence for the existence of black holes |journal=Classical and Quantum Gravity |volume=16 |issue=12A |pages=A3–A21 |date=1999 |arxiv=astro-ph/9912186 |doi=10.1088/0264-9381/16/12A/301 |bibcode=1999CQGra..16A...3C |url=https://cds.cern.ch/record/411555/files/9912186.pdf|s2cid=17677758 |archive-date=27 July 2018 |archive-url=https://web.archive.org/web/20180727052939/https://cds.cern.ch/record/411555/files/9912186.pdf |url-status=dead }}</ref>

The first strong candidate for a black hole, [[Cygnus X-1]], was discovered in this way by [[Charles Thomas Bolton]],<ref name="Bolton1972"/> [[Louise Webster]], and [[Paul Murdin]]<ref name="Webster1972"/> in 1972.<ref>{{cite web |last=Rolston |first=B. |date=10 November 1997 |url=http://news.utoronto.ca/bin/bulletin/nov10_97/art4.htm |archive-url=https://web.archive.org/web/20080502230214/http://news.utoronto.ca/bin/bulletin/nov10_97/art4.htm |archive-date=2 May 2008 |title=The First Black Hole |website=The bulletin |publisher=University of Toronto |access-date=11 March 2008}}</ref><ref name="Shipman1975"/>  Observations of rotation broadening of the optical star reported in 1986 lead to a mass estimate of 16 solar masses with 7 solar masses as the lower bound.<ref name="CMS1999"/> Additional observations and analysis lead to a 2011 report for the mass of {{val|14.1|1.0|u=solar mass}} for the black hole and {{val|19.2|1.9|u=solar mass}} for the optical companion.<ref>{{Cite journal |last=Orosz |first=Jerome A. |last2=McClintock |first2=Jeffrey E. |last3=Aufdenberg |first3=Jason P. |last4=Remillard |first4=Ronald A. |last5=Reid |first5=Mark J. |last6=Narayan |first6=Ramesh |last7=Gou |first7=Lijun |date=November 9, 2011 |title=THE MASS OF THE BLACK HOLE IN CYGNUS X-1 |journal=The Astrophysical Journal |volume=742 |issue=2 |pages=84 |doi=10.1088/0004-637x/742/2/84 |issn=0004-637X}}</ref>

In a class of X-ray binaries called soft X-ray transients, the companion star is of relatively low mass allowing for more accurate estimates of the black hole mass. These systems actively emit X-rays for only several months once every 10–50 years. During the period of low X-ray emission, called quiescence, the accretion disk is extremely faint, allowing detailed observation of the companion star during this period.<ref name="CMS1999" /> Numerous black hole candidates have been measured by this method.<ref>{{Cite journal |last=Corral-Santana |first=J. M. |last2=Casares |first2=J. |last3=Muñoz-Darias |first3=T. |last4=Bauer |first4=F. E. |last5=Martínez-Pais |first5=I. G. |last6=Russell |first6=D. M. |date=March 1, 2016 |title=BlackCAT: A catalogue of stellar-mass black holes in X-ray transients |url=https://www.aanda.org/articles/aa/abs/2016/03/aa27130-15/aa27130-15.html |journal=Astronomy & Astrophysics |language=en |volume=587 |pages=A61 |doi=10.1051/0004-6361/201527130 |issn=0004-6361}}</ref>

=== Quasi-periodic oscillations ===
{{main|Quasi-periodic oscillation}}

The X-ray emissions from accretion disks sometimes flicker at certain frequencies. These signals are called [[quasi-periodic oscillation]]s and are thought to be caused by material moving along the inner edge of the accretion disk (the innermost stable circular orbit). As such their frequency is linked to the mass of the compact object. They can thus be used as an alternative way to determine the mass of candidate black holes.<ref>{{cite press release |title=NASA scientists identify smallest known black hole |publisher=[[Goddard Space Flight Center]] |date=1 April 2008 |url=http://www.eurekalert.org/pub_releases/2008-04/nsfc-nsi040108.php |access-date=14 March 2009 |archive-url=https://web.archive.org/web/20081227195554/http://www.eurekalert.org/pub_releases/2008-04/nsfc-nsi040108.php |archive-date=27 December 2008 }}</ref>

==== Galactic nuclei ====
{{see also|Active galactic nucleus}}
[[File:X-RayFlare-BlackHole-MilkyWay-20140105.jpg|thumb|Detection of unusually bright [[X-ray]] flare from Sagittarius A*, a black hole in the centre of the Milky Way galaxy on 5{{nbsp}}January 2015<ref name="NASA-20150105">{{cite web |last1=Chou |first1=Felicia |last2=Anderson |first2=Janet |last3=Watzke |first3=Megan |date=5 January 2015 |title=RELEASE 15-001 – NASA's Chandra Detects Record-Breaking Outburst from Milky Way's Black Hole |url=http://www.nasa.gov/press/2015/january/nasa-s-chandra-detects-record-breaking-outburst-from-milky-way-s-black-hole/ |url-status=live |archive-url=https://web.archive.org/web/20150106100532/http://www.nasa.gov/press/2015/january/nasa-s-chandra-detects-record-breaking-outburst-from-milky-way-s-black-hole/ |archive-date=6 January 2015 |access-date=6 January 2015 |website=[[NASA]]}}</ref>]]

Astronomers use the term "active galaxy" to describe galaxies with unusual characteristics, such as unusual [[spectral line]] emission and very strong radio emission. Theoretical and observational studies have shown that the high levels of activity in the centers of these galaxies, regions called active galactic nuclei (AGN), may be explained by the presence of supermassive black holes, which can be millions of times more massive than stellar ones. The models of these AGN consist of a central black hole that may be millions or billions of times more massive than the [[Sun]]; a disk of [[interstellar gas]] and dust called an accretion disk; and two [[relativistic jet|jets]] perpendicular to the accretion disk.<ref name="krolik1999">{{cite book |first=J. H. |last=Krolik |date=1999 |title=Active Galactic Nuclei |publisher=Princeton University Press |isbn=978-0-691-01151-6 |at=Ch. 1.2 |url=https://books.google.com/books?id=oRK8otMiWIgC&q=Active+Galactic+Nuclei |access-date=16 October 2020 |archive-date=14 August 2021 |archive-url=https://web.archive.org/web/20210814220336/https://books.google.com/books?id=oRK8otMiWIgC&q=Active+Galactic+Nuclei |url-status=live }}</ref><ref name="sparkegallagher2000">{{cite book |first1=L. S. |last1=Sparke |author-link=Linda Sparke |first2=J. S. |last2=Gallagher |date=2000 |title=Galaxies in the Universe: An Introduction |publisher=Cambridge University Press |at=Ch. 9.1 |url=https://books.google.com/books?id=N8Hngab5liQC&q=Galaxies+in+the+Universe:+An+Introduction |isbn=978-0-521-59740-1 |access-date=16 October 2020 |archive-date=22 March 2022 |archive-url=https://web.archive.org/web/20220322141933/https://books.google.com/books?id=N8Hngab5liQC&q=Galaxies+in+the+Universe%3A+An+Introduction |url-status=live }}</ref>

Although supermassive black holes are expected to be found in most AGN, only some galaxies' nuclei have been more carefully studied in attempts to both identify and measure the actual masses of the central supermassive black hole candidates. Some of the most notable galaxies with supermassive black hole candidates include the [[Andromeda Galaxy]], [[Messier 32|M32]], [[Messier 87|M87]], [[NGC 3115]], [[NGC 3377]], [[NGC 4258]], [[NGC 4889]], [[NGC 1277]], [[OJ 287]], [[APM 08279+5255]] and the [[Sombrero Galaxy]].<ref name="kormendyrichstone1995">{{cite journal |first1=J. |last1=Kormendy |first2=D. |last2=Richstone |title=Inward Bound – The Search For Supermassive Black Holes In Galactic Nuclei |journal=Annual Review of Astronomy and Astrophysics |date=1995 |volume=33 |issue=1 |pages=581–624 |bibcode=1995ARA&A..33..581K |doi=10.1146/annurev.aa.33.090195.003053}}</ref>

It is now widely accepted that the centre of nearly every galaxy, not just active ones, contains a supermassive black hole.<ref name="King">{{cite journal |last=King |first=A. |title=Black Holes, Galaxy Formation, and the MBH-σ Relation |journal=The Astrophysical Journal Letters |volume=596 |issue=1 |pages=27–29 |date=2003 |doi=10.1086/379143 |arxiv=astro-ph/0308342|bibcode=2003ApJ...596L..27K|s2cid=9507887 }}</ref> The close observational correlation between the mass of this hole and the velocity dispersion of the host galaxy's [[galactic bulge|bulge]], known as the [[M–sigma relation]], strongly suggests a connection between the formation of the black hole and that of the galaxy itself.<ref name="msigma2000">{{cite journal |title=A Fundamental Relation Between Supermassive Black Holes and their Host Galaxies |last1=Ferrarese |first1=L. |last2=Merritt |first2=D. |author2-link=David Merritt |journal=The Astrophysical Journal Letters |volume=539 |issue=1 |pages=9–12 |date=2000 |bibcode=2000ApJ...539L...9F |doi=10.1086/312838 |arxiv=astro-ph/0006053 |s2cid=6508110}}</ref>

=== Microlensing ===
Another way the black hole nature of an object may be tested is through observation of effects caused by a strong gravitational field in their vicinity. One such effect is gravitational lensing: The deformation of spacetime around a massive object causes light rays to be deflected, such as light passing through an optic [[lens]]. Observations have been made of weak gravitational lensing, in which light rays are deflected by only a few [[arcsecond]]s. [[Microlensing]] occurs when the sources are unresolved and the observer sees a small brightening.{{Clarify|date=October 2025}} The turn of the millennium saw the first 3 candidate detections of black holes in this way,<ref>{{cite journal |last1=Bennett |first1=D. P. |last2=Becker |first2=A. C. |last3=Quinn |first3=J. L. |last4=Tomaney |first4=A. B. |last5=Alcock |first5=C. |last6=Allsman |first6=R. A. |last7=Alves |first7=D. R. |last8=Axelrod |first8=T. S. |last9=Calitz |first9=J. J. |last10=Cook |first10=K. H. |last11=Drake |first11=A. J. |last12=Fragile |first12=P. C. |last13=Freeman |first13=K. C. |last14=Geha |first14=M. |last15=Griest |first15=K. |date=1 November 2002 |title=Gravitational Microlensing Events Due to Stellar-Mass Black Holes |url=https://ui.adsabs.harvard.edu/abs/2002ApJ...579..639B/abstract |journal=The Astrophysical Journal |volume=579 |issue=2 |pages=639–659 |doi=10.1086/342225 |arxiv=astro-ph/0109467 |bibcode=2002ApJ...579..639B |issn=0004-637X}}</ref><ref>{{cite journal |last1=Mao |first1=Shude |last2=Smith |first2=Martin C. |last3=Woźniak |first3=P. |last4=Udalski |first4=A. |last5=Szymański |first5=M. |last6=Kubiak |first6=M. |last7=Pietrzyński |first7=G. |last8=Soszyński |first8=I. |last9=Żebruń |first9=K. |date=1 January 2002 |title=Optical Gravitational Lensing Experiment OGLE-1999-BUL-32: the longest ever microlensing event - evidence for a stellar mass black hole? |journal=Monthly Notices of the Royal Astronomical Society |volume=329 |issue=2 |pages=349–354 |doi=10.1046/j.1365-8711.2002.04986.x |doi-access=free |arxiv=astro-ph/0108312 |bibcode=2002MNRAS.329..349M |issn=0035-8711}}</ref> and in January 2022, astronomers reported the first confirmed detection of a microlensing event from an isolated black hole.<ref name="Sahu">{{cite journal |arxiv=2201.13296 |last1=Sahu |first1=K. C. |title=An Isolated Stellar-Mass Black Hole Detected Through Astrometric Microlensing |journal=Astrophysical Journal|date=2022|volume=933 |issue=1 |page=83 |doi=10.3847/1538-4357/ac739e |bibcode=2022ApJ...933...83S |s2cid=246430448 |doi-access=free }}</ref>

Another possibility for observing gravitational lensing by a black hole would be to observe stars orbiting the black hole. There are several candidates for such an observation in orbit around [[Sagittarius A*]].<ref name="Bozza">{{cite journal |arxiv=0911.2187 |last1=Bozza |first1=V. |title=Gravitational Lensing by Black Holes |journal=General Relativity and Gravitation |issue=9 |date=2010 |pages=2269–2300 |doi=10.1007/s10714-010-0988-2 |bibcode=2010GReGr..42.2269B |volume=42 |s2cid=118635353}}</ref>

{{clear}}

== Alternatives ==
{{see also|Exotic star}}

While there is a strong case for supermassive black holes, the model for stellar-mass black holes assumes of an upper limit for the mass of a neutron star: objects observed to have more mass are assumed to be black holes.  However, the properties of extremely dense matter are poorly understood. New exotic [[Phase (matter)|phases of matter]] could allow other kinds of massive objects.<ref name="CMS1999" /> A phase of free [[quark]]s at high density might allow the existence of dense quark stars,<ref>{{cite journal |last1=Kovacs |first1=Z. |last2=Cheng |first2=K. S. |last3=Harko |first3=T. |title=Can stellar mass black holes be quark stars? |journal=[[Monthly Notices of the Royal Astronomical Society]] |date=2009 |volume=400 |issue=3 |pages=1632–1642 |doi=10.1111/j.1365-2966.2009.15571.x |doi-access=free |arxiv=0908.2672 |bibcode=2009MNRAS.400.1632K |s2cid=18263809}}</ref> and some [[supersymmetry|supersymmetric]] models predict the existence of [[Q star]]s.<ref>{{cite arXiv |eprint=hep-ph/0612159 |first1=A. |last1=Kusenko |title=Properties and signatures of supersymmetric Q-balls |date=2006 }}</ref>{{Definition needed|date=October 2025}} Some extensions of the [[Standard Model]] posit the existence of [[preon]]s as fundamental building blocks of quarks and [[lepton]]s, which could hypothetically form [[preon star]]s.<ref>{{cite journal |last1=Hansson |first1=J. |last2=Sandin |first2=F. |title=Preon stars: a new class of cosmic compact objects |journal=Physics Letters B |volume=616 |issue=1–2 |pages=1–7 |date=2005 |doi=10.1016/j.physletb.2005.04.034 |arxiv=astro-ph/0410417 |bibcode=2005PhLB..616....1H |s2cid=119063004}}</ref> These hypothetical models could potentially explain a number of observations of stellar black hole candidates. However, it can be shown from arguments in general relativity that any such object will have a maximum mass.<ref name="CMS1999" />

Since the average density of a black hole inside its Schwarzschild radius is inversely proportional to the square of its mass, supermassive black holes are much less dense than stellar black holes. The average density of a {{Solar mass|{{10^|8}}}} black hole is comparable to that of water.<ref name="CMS1999" /> Consequently, the physics of matter forming a supermassive black hole is much better understood and the possible alternative explanations for supermassive black hole observations are much more mundane. For example, a supermassive black hole could be modelled by a large cluster of very dark objects. However, such alternatives are typically not stable enough to explain the supermassive black hole candidates.<ref name="CMS1999" />

A few theoretical objects have been conjectured to match observations of astronomical black hole candidates identically or near-identically,<ref name="Murk2023"/> but which function via a different mechanism.{{Clarify|date=October 2025}} These include the [[gravastar]],<ref>{{cite journal |last1=Mazur |first1=Pawel O. |last2=Mottola |first2=Emil |title=Gravitational vacuum condensate stars |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=101 |issue=26 |date=2004 |pages=9545–9550 |doi=10.1073/pnas.0402717101 |doi-access=free |pmid=15210982 |pmc=470711 |arxiv=gr-qc/0407075 |bibcode=2004PNAS..101.9545M |s2cid=2607263}}</ref> the [[black star (semiclassical gravity)|black star]],<ref>{{cite news |last1=Choi |first1=Charles Q. |title=Black Hole Pretenders Could Really Be Bizarre Quantum Stars |url=https://www.scientificamerican.com/article/black-hole-pretenders-could-really-be-bizarre-quantum-stars/ |access-date=17 March 2018 |work=Scientific American |date=2018 |archive-date=17 June 2019 |archive-url=https://web.archive.org/web/20190617164631/https://www.scientificamerican.com/article/black-hole-pretenders-could-really-be-bizarre-quantum-stars/ |url-status=live }}</ref> related [[nestar]]<ref name="SA-20240220">{{cite news |last=McRae |first=Mike |title=Bubble-Like 'Stars Within Stars' Could Explain Black Hole Weirdness |url=https://www.sciencealert.com/bubble-like-stars-within-stars-could-explain-black-hole-weirdness |date=20 February 2024 |work=[[ScienceAlert]] |url-status=live |archive-url=https://archive.today/20240220150012/https://www.sciencealert.com/bubble-like-stars-within-stars-could-explain-black-hole-weirdness |archive-date=20 February 2024 |access-date=20 February 2024 }}</ref> and the [[dark-energy star]].<ref>{{cite journal |last1=Ball |first1=Philip |title=Black holes 'do not exist' |journal=Nature |date=31 March 2005 |doi=10.1038/news050328-8}}</ref>

== Open questions ==
=== Entropy and thermodynamics ===
{{further|Black hole thermodynamics|Bekenstein bound}}
{{Image frame|content={{bigmath|1=''S'' = {{sfrac|1|4}} {{sfrac|''c''{{sup|3}}''k'' |''Għ''}} ''A''}}|caption=The formula for the Bekenstein–Hawking entropy ({{mvar|S}}) of a black hole, which depends on the area of the black hole ({{mvar|A}}). The constants are the [[speed of light]] ({{mvar|c}}), the [[Boltzmann constant]] ({{mvar|k}}), [[Newton's constant]] ({{mvar|G}}), and the [[reduced Planck constant]] ({{mvar|ħ}}). In Planck units, this reduces to {{math|1=''S'' = {{sfrac|''A''|4}}}}.|width=220}}

In 1971, Hawking showed under general conditions<ref group=Note>In particular, he assumed that all matter satisfies the [[weak energy condition]].</ref> that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and merge.<ref>{{cite journal |last=Hawking |first=S. W. |title=Gravitational Radiation from Colliding Black Holes |journal=Physical Review Letters |volume=26 |issue=21 |pages=1344–1346 |date=1971 |doi=10.1103/PhysRevLett.26.1344 |bibcode=1971PhRvL..26.1344H}}</ref> This result, now known as the [[second law of black hole mechanics]], is remarkably similar to the [[second law of thermodynamics]], which states that the total entropy of an isolated system can never decrease. As with classical objects at [[absolute zero]] temperature, it was assumed that black holes had zero entropy. If this were the case, the second law of thermodynamics would be violated by entropy-laden matter entering a black hole, resulting in a decrease in the total entropy of the universe. Therefore, Bekenstein proposed that a black hole should have an entropy, and that it should be proportional to its horizon area.<ref name="wald99">{{cite journal |last=Wald |first=R. M. |title=The Thermodynamics of Black Holes |journal=Living Reviews in Relativity |volume=4 |issue=1 |article-number=6 |date=2001 |arxiv=gr-qc/9912119 |bibcode=2001LRR.....4....6W |doi=10.12942/lrr-2001-6 |doi-access=free |pmid=28163633 |pmc=5253844}}</ref>

The link with the laws of thermodynamics was further strengthened{{how|date=October 2025}} by Hawking's discovery in 1974 that quantum field theory predicts that a black hole radiates [[blackbody radiation]] at a constant temperature. This seemingly causes a violation of the second law of black hole mechanics, since the radiation will carry away energy from the black hole causing it to shrink. The radiation also carries away entropy, and it can be proven under general assumptions that the sum of the entropy of the matter surrounding a black hole and one quarter of the area of the horizon as measured in Planck units is in fact always increasing. This allows the formulation of the [[first law of black hole mechanics]] as an analogue of the [[first law of thermodynamics]], with the mass acting as energy, the surface gravity as temperature and the area as entropy.<ref name="wald99" />{{Clarify|date=October 2025}}

One puzzling feature is that the entropy of a black hole scales with its area rather than with its volume, since entropy is normally an [[extensive quantity]]{{Definition needed|date=October 2025}} that scales linearly with the volume of the system. This odd property led [[Gerard 't Hooft]] and [[Leonard Susskind]] to propose the [[holographic principle]], which suggests that anything that happens in a volume of spacetime can be described by data on the boundary of that volume.<ref>{{cite book|last='t Hooft|first=G.|title=Basics and Highlights in Fundamental Physics|publisher=[[World Scientific Publishing]]|year=2001|isbn=978-981-02-4536-8|editor-last=Zichichi|editor-first=A.|series=Subnuclear series|volume=37|pages=72–100|chapter=The Holographic Principle|bibcode=2001bhfp.conf...72T|doi=10.1142/9789812811585_0005|arxiv=hep-th/0003004|s2cid=119383028}}</ref>{{Explain|date=October 2025}}

Although general relativity can be used to perform a semiclassical calculation of black hole entropy, this situation is theoretically unsatisfying. In [[statistical mechanics]], entropy is understood as counting the number of microscopic configurations of a system that have the same macroscopic qualities, such as mass, charge, and pressure. Without a satisfactory theory of quantum gravity, one cannot perform such a computation for black holes.<ref>{{cite journal |last=Kiefer |first=C. |date=12 January 2006 |title=Quantum gravity: general introduction and recent developments |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.200651801-210 |journal=Annalen der Physik |language=en |volume=518 |issue=1–2 |pages=129–148 |doi=10.1002/andp.200651801-210 |issn=0003-3804|url-access=subscription }}</ref> Some progress has been made in various approaches to quantum gravity. In 1995, [[Andrew Strominger]] and [[Cumrun Vafa]] showed that counting the microstates of a specific supersymmetric black hole in string theory reproduced the Bekenstein–Hawking entropy.<ref>{{cite journal |last1=Strominger |first1=A. |last2=Vafa |first2=C. |title=Microscopic origin of the Bekenstein-Hawking entropy |journal=Physics Letters B |volume=379 |issue=1–4 |pages=99–104 |date=1996 |doi=10.1016/0370-2693(96)00345-0 |arxiv=hep-th/9601029 |bibcode=1996PhLB..379...99S |s2cid=1041890}}</ref> Since then, similar results have been reported for different black holes both in string theory and in other approaches to quantum gravity like [[loop quantum gravity]].<ref>{{cite book |last1=Carlip |first1=S. |title=Physics of Black Holes |volume=769 |pages=89–123 |date=2009 |doi=10.1007/978-3-540-88460-6_3 |arxiv=0807.4520 |series=Lecture Notes in Physics |isbn=978-3-540-88459-0|bibcode=2009LNP...769...89C |chapter=Black Hole Thermodynamics and Statistical Mechanics|location=Berlin |publisher=Springer |s2cid=15877702 }}</ref>

=== Information loss paradox ===
{{main|Black hole information paradox}}
{{unsolved|physics|Is physical information lost in black holes?}}

Because, according to the no-hair theorem, a black hole has only a few internal parameters, most of the information about the matter that went into forming the black hole is lost. Regardless of the type of matter which goes into a black hole, it appears that only information concerning the total mass, charge, and angular momentum are conserved. When black holes were thought to persist forever, this information loss was not problematic, as the information can be thought of as existing inside the black hole, inaccessible from the outside, but represented on the event horizon in accordance with the holographic principle.{{Explain|date=October 2025}} However, black holes slowly evaporate by emitting Hawking radiation. This radiation does not appear to carry any additional information about the matter that formed the black hole, meaning that this information appears to be gone forever.<ref name="PlayDice000">{{cite web |title=Does God Play Dice? |first=S. W. |last=Hawking |url=http://www.hawking.org.uk/does-god-play-dice.html |website=www.hawking.org.uk |access-date=14 March 2009 |archive-url=https://web.archive.org/web/20120111012413/http://www.hawking.org.uk/does-god-play-dice.html |archive-date=11 January 2012 }}</ref>

The question whether information is truly lost in black holes (the [[black hole information paradox]]) has divided the theoretical physics community. In quantum mechanics, loss of information corresponds to the violation of a property called [[unitarity (physics)|unitarity]], and it has been argued that loss of unitarity would also imply violation of conservation of energy,<ref name="giddings1995">{{cite conference |first=S. B. |last=Giddings |title=The black hole information paradox |arxiv=hep-th/9508151 |book-title=Particles, Strings and Cosmology |date=1995 |conference=Johns Hopkins Workshop on Current Problems in Particle Theory 19 and the PASCOS Interdisciplinary Symposium 5 |bibcode=1995hep.th....8151G}}</ref> though this has also been disputed.<ref name="unruh2017"/> Over recent years evidence has been building that indeed information and unitarity are preserved in a full quantum gravitational treatment of the problem.<ref>{{cite conference |first=S. D. |last=Mathur |title=The information paradox: conflicts and resolutions |journal=Pramana |date=2011 |volume=79 |issue=5 |pages=1059–1073 |conference=XXV International Symposium on Lepton Photon Interactions at High Energies |arxiv=1201.2079 |bibcode=2012Prama..79.1059M |doi=10.1007/s12043-012-0417-z}}</ref>

One attempt to resolve the black hole information paradox is known as [[black hole complementarity]].{{More detail needed}} In 2012, the "[[Firewall (physics)|firewall paradox]]" was introduced with the goal of demonstrating that black hole complementarity fails to solve the information paradox. According to [[quantum field theory in curved spacetime]], a [[Black-body radiation|single emission]] of Hawking radiation involves two mutually [[quantum entanglement|entangled]] particles. The outgoing particle escapes and is emitted as a quantum of Hawking radiation; the infalling particle is swallowed by the black hole.{{dubious |reason=This is an oversimplified understanding of Hawking radiation that isn't really accurate|date=October 2025}} Assume a black hole formed a finite time in the past and will fully evaporate away in some finite time in the future. Then, it will emit only a finite amount of information encoded within its Hawking radiation. According to research by physicists like [[Don Page (physicist)|Don Page]]<ref>{{cite journal |last1=Page |first1=Don N. |title=Information in black hole radiation |journal=[[Phys. Rev. Lett.]] |date=1993 |volume=71 |issue=23 |pages=3743–3746 |doi=10.1103/PhysRevLett.71.3743 |pmid=10055062 |bibcode=1993PhRvL..71.3743P |arxiv=hep-th/9306083 |citeseerx=10.1.1.267.174|s2cid=9363821 }}</ref><ref>{{cite journal |last1=Page |first1=Don N. |title=Average entropy of a subsystem |journal=[[Phys. Rev. Lett.]] |date=1993 |volume=71 |issue=9 |pages=1291–1294 |doi=10.1103/PhysRevLett.71.1291 |pmid=10055503 |bibcode=1993PhRvL..71.1291P |arxiv=gr-qc/9305007 |citeseerx=10.1.1.339.7694|s2cid=17058654 }}</ref> and Leonard Susskind, there will eventually be a time by which an outgoing particle must be entangled with all the Hawking radiation the black hole has previously emitted.{{Explain|date=October 2025}}

This seemingly creates a paradox: a principle called "[[monogamy of entanglement]]" requires that, like any quantum system, the outgoing particle cannot be fully entangled with two other systems at the same time; yet here the outgoing particle appears to be entangled both with the infalling particle and, independently, with past Hawking radiation.<ref>{{cite journal |last1=Merali |first1=Zeeya |title=Astrophysics: Fire in the hole! |journal=Nature |date=3 April 2013 |volume=496 |issue=7443 |pages=20–23 |doi=10.1038/496020a |pmid=23552926 |bibcode=2013Natur.496...20M |doi-access=free}}</ref> In order to resolve this contradiction, physicists may eventually be forced to give up one of three time-tested principles: Einstein's equivalence principle, unitarity, or local quantum field theory. One possible solution, which violates the equivalence principle, is that a "firewall"{{definition needed|date=October 2025}} destroys incoming particles at the event horizon.<ref>{{cite journal | last1 = Amheiri | first1 = Ahmed | last2 = Marolf | first2 = Donald | last3 = Polchinski | first3 = Joseph | last4 = Sully | first4 = James | title = Black holes: Complementarity or Firewalls? | journal = Journal of High Energy Physics | date = 2013 | volume = 2013 | issue = 2 | page = 62 | doi = 10.1007/JHEP02(2013)062| arxiv = 1207.3123 | bibcode = 2013JHEP...02..062A | s2cid = 55581818 }}</ref> In general, which—if any—of these assumptions should be abandoned remains a topic of debate.<ref name="unruh2017">{{cite journal|first1=William G. |last1=Unruh |first2=Robert M. |last2=Wald |author-link1=W. G. Unruh |author-link2=Robert Wald |title=Information loss |journal=[[Reports on Progress in Physics]] |year=2017 |volume=80 |issue=9 |page=092002 |doi=10.1088/1361-6633/aa778e |pmid=28585922 |arxiv=1703.02140 |bibcode=2017RPPh...80i2002U|s2cid=39957660 }}</ref>

== In science fiction ==
{{main|Black holes in fiction}}

[[Christopher Nolan]]'s 2014 science fiction epic ''[[Interstellar (film)|Interstellar]]'' features a black hole known as Gargantua, which is the central object of a planetary system in a distant galaxy. Humanity accessed this system via a [[wormhole]] in the outer [[Solar System|solar system]], near [[Saturn]].

== See also ==
{{portal|Astronomy|History of science|Mathematics|Physics|Stars}}
{{div col|colwidth=18em}}
* [[Black brane]] or [[Black string]]
* [[Black Hole Initiative]]
* [[Black hole starship]]
* [[Black holes in fiction]]
* [[Blanet]]
* [[BTZ black hole]]
* [[Dark star (dark matter)]]
* [[Golden binary]]
* [[Hypothetical black hole (disambiguation)]]
* [[Kugelblitz (astrophysics)]]
* [[List of black holes]]
* [[List of nearest black holes]]
* [[Outline of black holes]]
* [[Planck star]]
* [[Sonic black hole]]
* [[Susskind-Hawking battle]]
* [[Timeline of black hole physics]]
* [[Virtual black hole]]
* [[White hole]]
{{div col end}}

== Notes ==
{{reflist|group="Note"}}

== References ==
{{reflist}}

== Sources ==
* {{cite book |last1=Carroll |first1=Sean M. | author-link = Sean M. Carroll |title=Spacetime and Geometry |date=2004 |publisher=Addison Wesley |isbn=978-0-8053-8732-2}}, the lecture notes on which the book was based are available for free from Sean Carroll's [https://www.preposterousuniverse.com/spacetimeandgeometry/ website] {{Webarchive|url=https://web.archive.org/web/20170323013522/http://www.preposterousuniverse.com/spacetimeandgeometry/ |date=23 March 2017 }}
* {{cite book |last1=Hawking |first1=S. W. |last2=Ellis |first2=G. F. R. |author-link1=Stephen Hawking | author2-link = George F. R. Ellis |title=Large Scale Structure of space time |publisher=Cambridge University Press |date=1973 |url=https://books.google.com/books?id=QagG_KI7Ll8C |isbn=978-0-521-09906-6 |access-date=16 May 2020 |archive-date=21 July 2020 |archive-url=https://web.archive.org/web/20200721064932/https://books.google.com/books?id=QagG_KI7Ll8C |url-status=live }}
* {{cite book |last1=Misner |first1=Charles |last2=Thorne |first2=Kip S. |last3=Wheeler |first3=John |author1-link=Charles W. Misner |author2-link=Kip Thorne |author3-link=John Archibald Wheeler |title=Gravitation |publisher=W. H. Freeman and Company |date=1973 |isbn=978-0-7167-0344-0}}
* {{Cite book |last1=Thorne |first1=Kip S. |author-link=Kip Thorne |title=Black Holes and Time Warps |publisher=Norton, W. W. & Company, Inc |date=1994 |isbn=978-0-393-31276-8|title-link=Black Holes and Time Warps}}
* {{cite book |last=Wald |first=Robert M. |author-link=Robert Wald |title=General Relativity |publisher=University of Chicago Press |date=1984 |isbn=978-0-226-87033-5 |url=https://books.google.com/books?id=9S-hzg6-moYC |access-date=23 February 2016 |archive-date=11 August 2016 |archive-url=https://web.archive.org/web/20160811035125/https://books.google.com/books?id=9S-hzg6-moYC |url-status=live }}
* {{cite book |last=Wheeler |first=J. Craig | author-link = J. Craig Wheeler |title=Cosmic Catastrophes |edition=2nd |publisher=Cambridge University Press |date=2007 |isbn=978-0-521-85714-7}}

== Further reading ==
=== Popular reading ===
{{refbegin}}
* {{Cite book |last1=Begelman |first1=Mitchell C. |url=https://books.google.com/books?id=ZPwAEAAAQBAJ |title=Gravity's fatal attraction: black holes in the universe |last2=Rees |first2=Martin J. |date=2021 |publisher=Cambridge University Press |isbn=978-1-108-87112-9 |edition=3rd |location=Cambridge, United Kingdom ; New York, NY}}
* {{cite book |last1=Ferguson |first1=Kitty |title=Black Holes in Space-Time |publisher=Watts Franklin |date=1991 |isbn=978-0-531-12524-3 |ref=none}}
* {{cite book |first1=Stephen |last1=Hawking |author1-link=Stephen Hawking |title=A Brief History of Time |publisher=Bantam Books, Inc |date=1988 |isbn=978-0-553-38016-3|title-link=A Brief History of Time  |ref=none}}
* {{cite book |first1=Stephen |last1=Hawking |author1-link=Stephen Hawking |first2=Roger |last2=Penrose |author2-link=Roger Penrose |title=The Nature of Space and Time |date=1996 |publisher=Princeton University Press |isbn=978-0-691-03791-2 |url=https://books.google.com/books?id=LstaQTXP65cC |ref=none |access-date=16 May 2020 |archive-date=18 October 2021 |archive-url=https://web.archive.org/web/20211018031528/https://books.google.com/books?id=LstaQTXP65cC |url-status=live }}
* {{cite book |last1=Levin |first1=Janna |title=Black hole survival guide |date=2020 |publisher=Alfred A. Knopf |location=New York |isbn=978-0-525-65822-1 |url=https://books.google.com/books?id=9rITEAAAQBAJ |access-date=6 November 2021 |archive-date=22 March 2022 |archive-url=https://web.archive.org/web/20220322141933/https://www.google.com/books/edition/Black_Hole_Survival_Guide/9rITEAAAQBAJ?hl=en&gbpv=1&dq=janna+levin&printsec=frontcover |url-status=live }}
* {{cite book |last1=Melia |first1=Fulvio |author1-link=Fulvio Melia |title=The Black Hole at the Center of Our Galaxy |publisher=Princeton U Press |date=2003 |isbn=978-0-691-09505-9 |url-access=registration |url=https://archive.org/details/blackholeatcente0000meli |ref=none }}
* {{cite book |last1=Melia |first1=Fulvio |title=The Edge of Infinity. Supermassive Black Holes in the Universe |publisher=Cambridge U Press |date=2003 |isbn=978-0-521-81405-8 |url-access=registration |url=https://archive.org/details/edgeofinfinitysu00meli |ref=none }}
* {{cite book |last1=Pickover |first1=Clifford |title=Black Holes: A Traveler's Guide |publisher=Wiley, John & Sons, Inc |date=1998 |isbn=978-0-471-19704-1 |ref=none}}
* {{Cite book |last=Susskind |first=Leonard |author-link=Leonard Susskind |title=The black hole war: my battle with Stephen Hawking to make the world safe for quantum mechanics |title-link=The Black Hole War |date=2008 |publisher=Little, Brown |isbn=978-0-316-01640-7 |edition=1st |location=New York |oclc=181603165 |ref=none}}
{{refend}}

=== University textbooks and monographs ===
{{refbegin}}
* {{Cite book |last=Carter |first=B. |author-link=Brandon Carter |title=Black holes |date=1973 |publisher=Gordon and Breach |isbn=978-0-677-15610-1 |editor-last=DeWitt-Morette |editor-first=Cécile |location=New York |chapter=Black hole equilibrium states |ref=none |editor-last2=DeWitt |editor-first2=Bryce S. |editor-link2=Bryce De Witt}}
* {{cite book |last1=Chandrasekhar |first1=Subrahmanyan |author-link1=Subrahmanyan Chandrasekhar |title=Mathematical Theory of Black Holes |publisher=Oxford University Press |date=1999 |isbn=978-0-19-850370-5  |ref=none}}
* {{cite book |doi=10.1007/978-94-011-5139-9 |title=Black Hole Physics |series=Fundamental Theories of Physics |year=1998 |volume=96 |isbn=978-0-7923-5146-7 |ref=none |last1=Frolov |first1=Valeri P. |last2=Novikov |first2=Igor D. }}
* {{cite book |last1=Frolov |first1=Valeri P. |last2=Zelnikov |first2=Andrei |title=Introduction to Black Hole Physics |publisher=Oxford University Press |date=2011 |location=Oxford |url=https://books.google.com/books?id=r_l5AK9DdXsC&pg=PA34 |isbn=978-0-19-969229-3 |zbl=1234.83001 |ref=none |access-date=2 January 2022 |archive-date=22 March 2022 |archive-url=https://web.archive.org/web/20220322142008/https://books.google.com/books?id=r_l5AK9DdXsC&pg=PA34 |url-status=live }}
* {{cite book |last1=Melia |first1=Fulvio |author1-link=Fulvio Melia |title=The Galactic Supermassive Black Hole |publisher=Princeton U Press |date=2007 |isbn=978-0-691-13129-0  |ref=none}}
* {{cite book |last1=Taylor |first1=Edwin F. |last2=Wheeler |first2=John Archibald |author2-link=John Archibald Wheeler |title=Exploring Black Holes |publisher=Addison Wesley Longman |date=2000 |isbn=978-0-201-38423-9  |ref=none}}
* {{cite book |last1=Wald |first1=Robert M. |title=Space, Time, and Gravity: The Theory of the Big Bang and Black Holes |publisher=University of Chicago Press |date=1992 |isbn=978-0-226-87029-8  |ref=none}}
* {{cite journal |doi=10.4249/scholarpedia.4277|bibcode=2008SchpJ...3.4277C|title=Black holes|year=2008|last1=Price|first1=Richard|last2=Creighton|first2=Teviet|journal=Scholarpedia|volume=3|issue=1|page=4277|doi-access=free  |ref=none}}
{{refend}}

=== Review papers ===
{{refbegin}}
* {{cite arXiv |eprint=hep-ph/0511217 |last1=Hughes |first1=Scott A. |title=Trust but verify: The case for astrophysical black holes |date=2005  |ref=none}} Lecture notes from 2005 [[SLAC]] Summer Institute.
* {{cite journal |last1=Gallo |first1=Elena |last2=Marolf |first2=Donald |doi=10.1119/1.3056569 |title=Resource Letter BH-2: Black Holes |date=2009 |issue=4 |pages=294–307 |volume=77 |journal=American Journal of Physics |arxiv=0806.2316 |bibcode=2009AmJPh..77..294G |s2cid=118494056}}
* {{cite journal |last1=Cardoso |first1=Vitor |last2=Pani |first2=Paolo |title=Testing the nature of dark compact objects: a status report |journal=Living Reviews in Relativity |volume=22 |issue=1 |page=4 |year=2019 |doi=10.1007/s41114-019-0020-4 |arxiv=1904.05363 |bibcode=2019LRR....22....4C |s2cid=256465740}}
* {{cite journal |last1=Mann |first1=Robert B. |last2=Murk |first2=Sebastian |last3=Terno |first3=Daniel R. |title=Black holes and their horizons in semiclassical and modified theories of gravity |journal=International Journal of Modern Physics D |volume=31 |issue=9 |pages=2230015–2230276 |year=2022 |doi=10.1142/S0218271822300154 |arxiv=2112.06515 |bibcode=2022IJMPD..3130015M |s2cid=245123647}}
{{refend}}

== External links ==
<!--Please do not add any more external links here. Wikipedia is not a collection of links. For details, please see [[Wikipedia:External links]] and [[WP:LINKFARM-->
{{Sister project links|d=Q589|voy=no|wikt=black hole|c=Category:Black holes|n=Category:Black holes|s=no|b=General Astronomy/Black holes/Introduction}}
{{Scholia}}
* {{In Our Time|Black Holes|p00547f4|Black_Holes}}
* ''[[Stanford Encyclopedia of Philosophy]]'': "[https://plato.stanford.edu/entries/spacetime-singularities/ Singularities and Black Holes]" by Erik Curiel and Peter Bokulich.
* [https://hubblesite.org/contents/articles/black-holes.html Black Holes: Gravity's Relentless Pull] – Interactive multimedia Web site about the physics and astronomy of black holes from the Space Telescope Science Institute (HubbleSite)
* [[ESA]]'s [https://www.esa.int/gsp/ACT/phy/Projects/Blackholes/WebGL.html Black Hole Visualization] {{Webarchive|url=https://web.archive.org/web/20190503070935/https://www.esa.int/gsp/ACT/phy/Projects/Blackholes/WebGL.html |date=3 May 2019 }}
* [https://apod.nasa.gov/htmltest/gifcity/bh_pub_faq.html Frequently Asked Questions (FAQs) on Black Holes]
* [https://web.archive.org/web/19980118051503/http://casa.colorado.edu/~ajsh/schwp.html Schwarzschild Geometry]
* [https://www.nytimes.com/2021/04/22/science/black-holes-astrophysics-names.html Black holes - basic (NYT; April 2021)]

=== Videos ===
* [https://www.eso.org/public/videos/eso0846b/ 16-year-long study tracks stars orbiting Sagittarius A*]
* [https://web.archive.org/web/20040925044354/http://www.mpe.mpg.de/ir/GC/index.php Movie of Black Hole Candidate from Max Planck Institute]
* {{cite journal |last1=Cowen |first1=Ron |title=3D simulations of colliding black holes hailed as most realistic yet |journal=Nature |date=20 April 2015 |doi=10.1038/nature.2015.17360 |doi-access=free |ref=none}}
* [https://www.bbc.com/news/science-environment-35524440 Computer visualisation of the signal detected by LIGO]
* [https://www.youtube.com/watch?v=I_88S8DWbcU Two Black Holes Merge into One (based upon the signal GW150914)]

{{Black holes}}
{{Relativity}}
{{String theory topics}}
{{Authority control}}

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