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Schwarzschild radius

2025-10-31T16:39:33Z

2405:6E00:63A:E7E9:FC59:A773:B530:FF58:

{{Short description|Radius of the event horizon of a Schwarzschild black hole}}
{{use dmy dates |date=September 2023}}

[[File:Triangle of everything simplified 2 triangle of everything - Planck Units.png | thumb|upright=1.5 | In this mass–radius plot, the Schwarzschild radius is shown as a lower limit on radii of isolated objects, and below the [[Compton limit]] quantum effects become significant. The [[Hubble radius]] gives a very rough sense of the scale of the observable Universe.]]

The '''Schwarzschild radius''' is a parameter in the [[Schwarzschild solution]] to [[Einstein's field equation]]s that corresponds to the [[radius]] of a sphere in flat space that has the same surface area as that of the [[event horizon]] of a Schwarzschild [[black hole]] of a given mass. It is a characteristic quantity that may be associated with any quantity of mass. The Schwarzschild radius was named after the German astronomer [[Karl Schwarzschild]], who calculated this solution for the theory of [[general relativity]] in 1916.

The Schwarzschild radius is given as
<math display="block"> r_\text{s} = \frac{2 G M}{c^2} ,</math>
where ''G'' is the [[Newtonian constant of gravitation]], ''M'' is the mass of the object, and ''c'' is the [[speed of light]].<ref>{{cite book |last=Kutner |first=Marc Leslie |url=https://archive.org/details/astronomyphysica00kutn/ |title=Astronomy: a physical perspective |date=2003 |publisher=[[Cambridge University Press]] |isbn=978-0-521-82196-4 |edition=2nd |location=Cambridge, U.K.; New York |pages=148}}</ref><ref>{{Cite book |last=Guidry |first=M. W. |title=Modern general relativity: black holes, gravitational waves, and cosmology |date=2019 |publisher=Cambridge University Press |isbn=978-1-107-19789-3 |location=Cambridge; New York, NY |pages=92}}</ref>

== History ==
In 1916, [[Karl Schwarzschild]] obtained an exact solution<ref>{{cite journal | url=https://ui.adsabs.harvard.edu/abs/1916SPAW.......189S/abstract |bibcode=1916SPAW.......189S |title=Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie |last1=Schwarzschild |first1=Karl |journal=Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften |date=1916 |page=189 }}</ref><ref>{{cite journal |url=https://ui.adsabs.harvard.edu/abs/1916skpa.conf..424S/abstract |page=424 |bibcode=1916skpa.conf..424S |title=Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie |last1=Schwarzschild |first1=Karl |journal=Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin |date=1916 }}</ref> to the [[Einstein field equations]] for the gravitational field outside a non-rotating, spherically symmetric body with mass <math>M</math> (see ''[[Schwarzschild metric]]''). The solution contained terms of the form {{tmath|1= 1 - r_\text{s}/r }} and {{tmath|1= \textstyle \frac{1}{1 - r_\text{s}/r} }}, which have [[Mathematical singularity|singularities]] at <math>r = 0</math> and <math> r=r_\text{s}</math> respectively. The <math>r_\text{s}</math> has come to be known as the ''Schwarzschild radius''. The physical significance of these singularities was debated for decades. It was found that the one at <math> r = r_\text{s}</math> is a [[coordinate singularity]], meaning that it is an artifact of the particular system of coordinates that was used; while the one at <math>r=0</math> is a [[spacetime singularity]] and cannot be removed.<ref>{{cite book |last1=Wald |first1=Robert |title=General Relativity |url=https://archive.org/details/generalrelativit0000wald |url-access=registration |date=1984 |publisher=The University of Chicago Press |isbn=978-0-226-87033-5 |pages=[https://archive.org/details/generalrelativit0000wald/page/152 152–153]}}</ref> The Schwarzschild radius is nonetheless a physically relevant quantity, as noted above and below.

This expression had previously been calculated, using Newtonian mechanics, as the radius of a spherically symmetric body at which the [[escape velocity]] was equal to the speed of light. It had been identified in the 18th century by [[John Michell]]<ref name="Schaffer">{{cite journal |last1=Schaffer |first1=Simon |title=John Michell and Black Holes |journal=Journal for the History of Astronomy |date=1979 |volume=10 |pages=42–43 |url=http://adsbit.harvard.edu//full/1979JHA....10...42S/0000042.000.html |access-date=4 June 2018|bibcode=1979JHA....10...42S |doi=10.1177/002182867901000104 |s2cid=123958527 |url-access=subscription }}</ref> and [[Pierre-Simon Laplace]].<ref>{{cite journal |bibcode=2009JAHH...12...90M |url=http://www.narit.or.th/en/files/2009JAHHvol12/2009JAHH...12...90M.pdf |archive-url=https://web.archive.org/web/20140502005017/http://www.narit.or.th/en/files/2009JAHHvol12/2009JAHH...12...90M.pdf |archive-date=2 May 2014 |title=Michell, Laplace and the origin of the black hole concept |last1=Montgomery |first1=Colin |last2=Orchiston |first2=Wayne |last3=Whittingham |first3=Ian |journal=Journal of Astronomical History and Heritage |date=2009 |volume=12 |issue=2 |page=90 |doi=10.3724/SP.J.1440-2807.2009.02.01 |s2cid=55890996 }}</ref>

== Parameters ==
The Schwarzschild radius of an object is proportional to its mass. Accordingly, the [[Sun]] has a Schwarzschild radius of approximately {{convert|3.0|km|mi|abbr=on}},<ref name="Anderson">{{cite encyclopedia |title=V.C The Schwarzschild Field, Event Horizons, and Black Holes |encyclopedia=Encyclopedia of Physical Science and Technology (Third Edition) |editor1-last=Meyer |editor1-first=Robert A. |date=2001 |last=Anderson |first=James L. |publisher=[[Academic Press]] |location=Cambridge, Massachusetts |isbn=978-0-12-227410-7 |url=https://www.sciencedirect.com/topics/physics-and-astronomy/schwarzschild-radius |access-date=23 October 2023}}</ref> whereas [[Earth]]'s is approximately {{convert|9|mm|in|abbr=on}}<ref name="Anderson" /> and the [[Moon]]'s is approximately {{convert|0.1|mm|in|abbr=on|sigfig=1}}.

{| class="wikitable mw-collapsible mw-collapsed" style="text-align:right;"
|+Schwarzschild radii
|-
! style="text-align:left;" | Object
! Mass <math display="inline">M</math>
! Schwarzschild radius{{br}}<math display="inline">\frac{2GM}{c^2}</math>
! Actual radius <math display="inline">r</math>
! Schwarzschild density{{br}}<math display="inline">\frac{3c^6}{32\pi G^3M^2}</math> or <math display="inline">\frac{3c^2}{8\pi Gr^2}</math>
|-
| style="text-align:left;" | [[Milky Way]]
| {{val|1.6|e=42|u=kg}}
| {{val|2.4|e=15|u=m}} ({{val|0.25|u=[[light-year|ly]]}})
| {{val|5|e=20|u=m}} ({{val|52900|u=[[light-year|ly]]}})
| {{val|0.000029|u=kg/m3}}
|-
| style="text-align:left;" | [[Supermassive black hole|SMBH]] in [[Phoenix Cluster#Supermassive black hole|Phoenix A]] (one of the largest [[List of most massive black holes|known black holes]])
| {{val|2|e=41|u=kg}}
| {{val|3|e=14|u=m}} (~2000 [[astronomical unit|AU]])
|
| {{val|0.0018|u=kg/m3}}
|-
| style="text-align:left;" | [[Ton 618]]
| {{val|1.3|e=41|u=kg}}
| {{val|1.9|e=14|u=m}} (~1300 [[astronomical unit|AU]])
|
| {{val|0.0045|u=kg/m3}}
|-
| style="text-align:left;" | [[Supermassive black hole|SMBH]] in [[NGC 4889]]
| {{val|4.2|e=40|u=kg}}
| {{val|6.2|e=13|u=m}} (~410 [[astronomical unit|AU]])
|
| {{val|0.042|u=kg/m3}}
|-
| style="text-align:left;" | [[Supermassive black hole|SMBH]] in [[Messier 87]]<ref name="Event Horizon Telescope Collaboration et al. 2019">{{cite journal
| last1 = Event Horizon Telescope Collaboration
| date = 2019
| title = First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
| journal = [[Astrophysical Journal Letters]]
| volume = 875
| issue = 1
| pages = L1
| bibcode = 2019ApJ...875L...1E
| doi = 10.3847/2041-8213/AB0EC7
| arxiv = 1906.11238
| doi-access = free
}}
{{val|6.5|(7)|e=9|u={{Solar mass}}}} = {{val|1.29|(14)|e=40|u=kg}}.
</ref>
| {{val|1.3|e=40|u=kg}}
| {{val|1.9|e=13|u=m}} (~130 [[astronomical unit|AU]])
|
| {{val|0.44|u=kg/m3}}
|-
| style="text-align:left;" | [[Supermassive black hole|SMBH]] in [[Andromeda Galaxy]]<ref name="Bender et al 2005">
{{cite journal
| display-authors = 3
| last1 = Bender | first1 = Ralf
| last2 = Kormendy | first2 = John
| last3 = Bower | first3 = Gary
| last4 = Green | first4 = Richard
| last5 = Thomas | first5 = Jens
| last6 = Danks | first6 = Anthony C.
| last7 = Gull | first7 = Theodore
| last8 = Hutchings | first8 = J. B.
| last9 = Joseph | first9 = C. L.
| last10 = Kaiser | first10 = M. E.
| last11 = Lauer | first11 = Tod R.
| last12 = Nelson | first12 = Charles H.
| last13 = Richstone | first13 = Douglas
| last14 = Weistrop | first14 = Donna
| last15 = Woodgate | first15 = Bruce
| date = 2005
| title = HST STIS Spectroscopy of the Triple Nucleus of M31: Two Nested Disks in Keplerian Rotation around a Supermassive Black Hole
| journal = [[Astrophysical Journal]]
| volume = 631
| issue = 1
| pages = 280–300
| bibcode = 2005ApJ...631..280B
| arxiv = astro-ph/0509839
| doi = 10.1086/432434
| s2cid = 53415285
}}
{{val|1.7|(6)|e=8|u={{Solar mass}}}} = {{val|0.34|(12)|e=39|u=kg}}.
</ref>
| {{val|3.4|e=38|u=kg}}
| {{val|5.0|e=11|u=m}} (3.3 [[astronomical unit|AU]])
|
| {{val|640|u=kg/m3}}
|-
| style="text-align:left;" | [[Sagittarius A*|Sagittarius A* (SMBH in Milky Way)]]<ref name="Ghez08" />
| {{val|8.26|e=36|u=kg}}
| {{val|1.23|e=10|u=m}} (0.08 [[astronomical unit|AU]])
|
| {{val|1.068|e=6|u=kg/m3}}
|-
| style="text-align:left;" |[[Supermassive black hole|SMBH]] in [[NGC 4395]]<ref>{{cite journal |last1=Peterson |first1=Bradley M. |last2=Bentz |first2=Misty C. |last3=Desroches |first3=Louis-Benoit |last4=Filippenko |first4=Alexei V. |last5=Ho |first5=Luis C. |last6=Kaspi |first6=Shai |last7=Laor |first7=Ari |last8=Maoz |first8=Dan |last9=Moran |first9=Edward C. |last10=Pogge |first10=Richard W. |last11=Quillen |first11=Alice C. |date=2005-10-20 |title=Multiwavelength Monitoring of the Dwarf Seyfert 1 Galaxy NGC 4395. I. A Reverberation-Based Measurement of the Black Hole Mass |journal=The Astrophysical Journal |volume=632 |issue=2 |pages=799–808 |doi=10.1086/444494 |arxiv=astro-ph/0506665 |bibcode=2005ApJ...632..799P |hdl=1811/48314 |s2cid=13886279 |issn=0004-637X}}</ref>
| {{val|7.1568|e=35|u=kg}}
| {{val|1.062|e=9|u=m}} (1.53 [[Solar radius|''R''⊙]])
|
| {{val|1.4230|e=8|u=kg/m3}}
|-
| style="text-align:left;" |Potential [[Intermediate-mass black hole|intermediate black hole]] in [[HCN-0.009-0.044]]<ref>{{cite web |last= |first= |date=1 March 2019 |title=Hiding black hole found |url=https://phys.org/news/2019-03-black-hole.html |access-date=2022-06-15 |website=[[phys.org]] |language=en}}</ref><ref>{{cite journal |doi=10.3847/2041-8213/aafb07 |doi-access=free |title=Indication of Another Intermediate-mass Black Hole in the Galactic Center |date=2019 |last1=Takekawa |first1=Shunya |last2=Oka |first2=Tomoharu |last3=Iwata |first3=Yuhei |last4=Tsujimoto |first4=Shiho |last5=Nomura |first5=Mariko |journal=The Astrophysical Journal |volume=871 |issue=1 |pages=L1 |arxiv=1812.10733 |bibcode=2019ApJ...871L...1T }}</ref>
| {{val|6.3616|e=34|u=kg}}
| {{val|9.44|e=8|u=m}} (14.8 [[Earth radius|''R''⊕]])
|
| {{val|1.8011|e=10|u=kg/m3}}
|-
| style="text-align:left;" |Resulting [[Intermediate-mass black hole|intermediate black hole]] from [[GW190521]] merger<ref>{{cite journal |last1=Abbott |first1=R. |last2=Abbott |first2=T. D. |last3=Abraham |first3=S. |last4=Acernese |first4=F. |last5=Ackley |first5=K. |last6=Adams |first6=C. |last7=Adhikari |first7=R. X. |last8=Adya |first8=V. B. |last9=Affeldt |first9=C. |last10=Agathos |first10=M. |last11=Agatsuma |first11=K. |date=2020-09-02 |title=Properties and Astrophysical Implications of the 150 ''M''⊙ Binary Black Hole Merger GW190521 |journal=The Astrophysical Journal |language=en |volume=900 |issue=1 |pages=L13 |doi=10.3847/2041-8213/aba493 |arxiv=2009.01190 |bibcode=2020ApJ...900L..13A |s2cid=221447444 |issn=2041-8213 |doi-access=free }}</ref>
| {{val|2.823|e=32|u=kg}}
| {{val|4.189|e=5|u=m}} (0.066 [[Earth radius|''R''⊕]])
|
| {{val|9.125|e=14|u=kg/m3}}
|-
| style="text-align:left;" | [[Sun]]
| {{val|1.99|e=30|u=kg}}
| {{val|2.95|e=3|u=m}}
| {{val|7.0|e=8|u=m}}
| {{val|1.84|e=19|u=kg/m3}}
|-
| style="text-align:left;" | [[Jupiter]]
| {{val|1.90|e=27|u=kg}}
| {{val|2.82|u=m}}
| {{val|7.0|e=7|u=m}}
| {{val|2.02|e=25|u=kg/m3}}
|-
| style="text-align:left;" | [[Saturn]]
| {{val|5.683|e=26|u=kg}}
| {{val|8.42|e=-1|u=m}}
| {{val|6.03|e=7|u=m}}
| {{val|2.27|e=26|u=kg/m3}}
|-
| style="text-align:left;" | [[Neptune]]
| {{val|1.024|e=26|u=kg}}
| {{val|1.52|e=-1|u=m}}
| {{val|2.47|e=7|u=m}}
| {{val|6.97|e=27|u=kg/m3}}
|-
| style="text-align:left;" | [[Uranus]]
| {{val|8.681|e=25|u=kg}}
| {{val|1.29|e=-1|u=m}}
| {{val|2.56|e=7|u=m}}
| {{val|9.68|e=27|u=kg/m3}}
|-
| style="text-align:left;" | [[Earth]]
| {{val|5.97|e=24|u=kg}}
| {{val|8.87|e=-3|u=m}}
| {{val|6.37|e=6|u=m}}
| {{val|2.04|e=30|u=kg/m3}}
|-
| style="text-align:left;" | [[Venus]]
| {{val|4.867|e=24|u=kg}}
| {{val|7.21|e=-3|u=m}}
| {{val|6.05|e=6|u=m}}
| {{val|3.10|e=30|u=kg/m3}}
|-
| style="text-align:left;" | [[Mars]]
| {{val|6.39|e=23|u=kg}}
| {{val|9.47|e=-4|u=m}}
| {{val|3.39|e=6|u=m}}
| {{val|1.80|e=32|u=kg/m3}}
|-
| style="text-align:left;" | [[Mercury (planet)|Mercury]]
| {{val|3.285|e=23|u=kg}}
| {{val|4.87|e=-4|u=m}}
| {{val|2.44|e=6|u=m}}
| {{val|6.79|e=32|u=kg/m3}}
|-
| style="text-align:left;" | [[Moon]]
| {{val|7.35|e=22|u=kg}}
| {{val|1.09|e=-4|u=m}}
| {{val|1.74|e=6|u=m}}
| {{val|1.35|e=34|u=kg/m3}}
|-
| style="text-align:left;" | [[Human]]
| {{val|70|u=kg}}
| {{val|1.04|e=-25|u=m}}
| ~ {{val|5|e=-1|u=m}}
| {{val|1.49|e=76|u=kg/m3}}
|-
| style="text-align:left;" | [[Planck mass]]
| {{val|2.18|e=-8|u=kg}}
| {{val|3.23|e=-35|u=m}} (2 [[Planck length|''l''P]])
| style="text-align:left;" |
| {{val|1.54|e=95|u=kg/m3}}
|}

== Derivation ==
{{main|Derivation of the Schwarzschild solution}}

== Black hole classification by Schwarzschild radius ==
{|class="wikitable" style="float:right; margin:0 0 0.5em 1em;"
|+ Black hole classifications
|-
! Class !! Approx. mass !! Approx. radius
|-
|[[Supermassive black hole]] ||style="text-align: center;"|10{{sup|5}}–10{{sup|11}} [[solar mass|''M''{{sub|Sun}}]] ||style="text-align: center;"|0.002–2000 [[Astronomical unit|AU]]
|-
|[[Intermediate-mass black hole]] ||style="text-align: center;"|{{val|e=3|u=''M''{{sub|Sun}}}} ||style="text-align: center;"| {{val|3000|u=km}} ≈ ''R''{{sub|[[Mars]]}}
|-
|[[Stellar black hole]] ||style="text-align: center;"|10 ''M''{{sub|Sun}} ||style="text-align: center;"|30 km
|-
|[[Micro black hole]] ||style="text-align: center;"|up to ''M''{{sub|[[Moon]]}} ||style="text-align: center;"|up to 0.1 mm
|}
Any object whose radius is smaller than its Schwarzschild radius is called a [[black hole]].<ref>{{Cite book |last=Zee |first=Anthony |title=Einstein Gravity in a Nutshell |date=2013 |publisher=Princeton University Press |isbn=978-0-691-14558-7 |edition=1 |series=In a Nutshell Series |location=Princeton}}</ref>{{rp|410}} The surface at the Schwarzschild radius acts as an [[event horizon]] in a non-rotating body (a [[rotating black hole]] operates slightly differently). Neither light nor particles can escape through this surface from the region inside, hence the name "black hole".

Black holes can be classified based on their Schwarzschild radius, or equivalently, by their density, where density is defined as mass of a black hole divided by the volume of its Schwarzschild sphere. As the Schwarzschild radius is linearly related to mass, while the enclosed volume corresponds to the third power of the radius, small black holes are therefore much more dense than large ones. The volume enclosed in the event horizon of the most massive black holes has an average density lower than main sequence stars.

=== Supermassive black hole ===
{{main|Supermassive black hole}}
A [[supermassive black hole]] (SMBH) is the largest type of black hole, though there are few official criteria on how such an object is considered so, on the order of hundreds of thousands to billions of solar masses. (Supermassive black holes up to 21 billion {{Solar mass|(2.1 × 1010)}} have been detected, such as [[NGC 4889]].)<ref>{{cite journal|title=Two ten-billion-solar-mass black holes at the centres of giant elliptical galaxies|last=McConnell|first=Nicholas J.|date=2011-12-08| journal=Nature|volume=480|issue=7376|doi=10.1038/nature10636|pmid = 22158244|pages=215–218|arxiv=1112.1078| bibcode=2011Natur.480..215M |s2cid=4408896}}</ref> Unlike [[Stellar black hole|stellar mass black holes]], supermassive black holes have comparatively low average densities. (Note that a (non-rotating) black hole is a spherical region in space that surrounds the singularity at its center; it is not the singularity itself.) With that in mind, the average density of a supermassive black hole can be less than the density of water.{{cn|date=February 2025}}

The Schwarzschild radius of a body is proportional to its mass and therefore to its volume, assuming that the body has a constant mass-density.<ref>{{cite book|author=Robert H. Sanders|title=Revealing the Heart of the Galaxy: The Milky Way and its Black Hole|url=https://books.google.com/books?id=C1dzAwAAQBAJ|year=2013|publisher=Cambridge University Press|isbn=978-1-107-51274-0| page=[https://books.google.com/books?id=C1dzAwAAQBAJ&pg=PA36 36]}}</ref> In contrast, the physical radius of the body is proportional to the cube root of its volume. Therefore, as the body accumulates matter at a given fixed density (in this example, {{val|997|ul=kg/m3}}, the density of water), its Schwarzschild radius will increase more quickly than its physical radius. When a body of this density has grown to around 136 million solar masses ({{Solar mass|1.36 × 108}}), its physical radius would be overtaken by its Schwarzschild radius, and thus it would form a supermassive black hole.

It is thought that supermassive black holes like these do not form immediately from the singular collapse of a cluster of stars. Instead they may begin life as smaller, stellar-sized black holes and grow larger by the accretion of matter, or even of other black holes.<ref>{{Cite journal|last1=Pacucci|first1=Fabio|last2=Loeb|first2=Abraham|date=2020-06-01|title=Separating Accretion and Mergers in the Cosmic Growth of Black Holes with X-Ray and Gravitational-wave Observations|bibcode=2020ApJ...895...95P|journal=The Astrophysical Journal|volume=895|issue=2|pages=95|doi=10.3847/1538-4357/ab886e|arxiv=2004.07246|s2cid=215786268 |doi-access=free }}</ref>

The Schwarzschild radius of the [[Sagittarius A*|supermassive black hole]] at the [[Galactic Center]] of the [[Milky Way]] is approximately 12 million kilometres.<ref name="Ghez08">
{{cite journal
| author = Ghez, A. M.
| display-authors=et al.
| title = Measuring Distance and Properties of the Milky Way's Central Supermassive Black Hole with Stellar Orbits
| journal = Astrophysical Journal
| date = December 2008
| volume = 689 | issue = 2 | pages = 1044–1062
| arxiv=0808.2870
| bibcode = 2008ApJ...689.1044G
| doi = 10.1086/592738
| s2cid=18335611
}}</ref> Its mass is about {{Solar mass|4.1 million}}.

=== Stellar black hole ===
{{main|Stellar black hole}}
Stellar black holes have much greater average densities than supermassive black holes. If one accumulates matter at [[nuclear density]] (the density of the nucleus of an atom, about 1018 [[kilogram per cubic metre|kg/m3]]; [[neutron star]]s also reach this density), such an accumulation would fall within its own Schwarzschild radius at about {{Solar mass|3}} and thus would be a [[stellar black hole]].{{cn|date=February 2025}}

=== Micro black hole ===
{{main|Micro black hole}}
A small mass has an extremely small Schwarzschild radius. A black hole of mass similar to that of [[Mount Everest]],<ref name="SST">{{cite web |url=http://chemist.sg/mole/Mount%20Everest%20M&Ms.pdf |title=How does the mass of one mole of M&M's compare to the mass of Mount Everest? |date=March 2003 |publisher=School of Science and Technology, Singapore |access-date=8 December 2014 |quote=If Mount Everest is assumed* to be a cone of height 8850 m and radius 5000 m, then its volume can be calculated using the following equation: volume <nowiki>=</nowiki> {{pi}}''r''2''h''/3 [...] Mount Everest is composed of granite, which has a density of {{val|2750|u=kg.m-3}}. |url-status=dead |archive-url=https://web.archive.org/web/20141210070657/http://chemist.sg/mole/Mount%20Everest%20M%26Ms.pdf |archive-date=10 December 2014}}</ref> {{val|6.3715e14|u=kg}}, would have a Schwarzschild radius much smaller than a [[nanometre]]. The Schwarzschild radius would be 2 × {{val|6.6738e-11|u=m3⋅kg−1⋅s−2}} × {{val|6.3715e14|u=kg}} / ({{val|299792458|u=m.s-1}})2 {{=}} {{val|9.46e-13|u=m}} {{=}} {{val|9.46e-4|u=nm}}. Its average density at that size would be so high that no known mechanism could form such extremely compact objects. Such black holes might possibly have been formed in an early stage of the evolution of the universe, just after the [[Big Bang]], when densities of matter were extremely high. Therefore, these hypothetical miniature black holes are called [[primordial black hole]]s.{{cn|date=February 2025}}

== Other uses ==

=== In gravitational time dilation ===

[[Gravitational time dilation]] near a large, slowly rotating, nearly spherical body, such as the Earth or Sun can be reasonably approximated as follows:<ref>{{Cite book |last=Keeton |first=Charles |url=https://books.google.com/books?id=PoQpBAAAQBAJ |title=Principles of astrophysics: using gravity and stellar physics to explore the cosmos |date=2014 |publisher=Springer |isbn=978-1-4614-9236-8 |series=Undergraduate Lecture Notes in Physics |location=New York |pages=208 }}</ref>
<math display="block"> \frac{t_r}{t} = \sqrt{1 - \frac{r_\mathrm{s}}{r}} </math>
where:
* {{var|tr}} is the elapsed time for an observer at radial coordinate ''r'' within the gravitational field;
* {{var|t}} is the elapsed time for an observer distant from the massive object (and therefore outside of the gravitational field);
* {{var|r}} is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object);
* {{math|''r''s}} is the Schwarzschild radius.

=== Compton wavelength intersection ===
The Schwarzschild radius ({{tmath|1= 2 G M/c^2 }}) of a given mass {{tmath|M}} equals twice its [[reduced Compton wavelength]] ({{tmath|1= \hbar/M c }}) when {{tmath|M}} equals one [[Planck mass]] ({{tmath|1= \textstyle M=\sqrt{\hbar c/G} }}); both are then equal to the [[Planck length]] (<math display="inline">\sqrt{\hbar G/c^3}</math>).

=== Calculating the maximum volume and radius possible given a density before a black hole forms ===
The Schwarzschild radius equation can be manipulated to yield an expression that gives the largest possible radius from an input density that doesn't form a black hole. Taking the input density as {{math| ''ρ''}},
: <math>r_\text{s} = \sqrt{\frac{3 c^{2}}{8 \pi G \rho}}.</math>

For example, the density of water is {{val|1000|u=kg/m3}}. This means the largest amount of water you can have without forming a black hole would have a radius of {{val|400920754|u=km}} (about 2.67 [[Astronomical unit|AU]]).

== See also ==
* [[Black hole]], a general survey
* [[Chandrasekhar limit]], a second requirement for black hole formation
* [[John Michell]]
Classification of black holes by type:
* [[Schwarzschild black hole|Static or Schwarzschild black hole]]
* [[Rotating black hole|Rotating or Kerr black hole]]
* [[Charged black hole|Charged black hole or Newman black hole and Kerr–Newman black hole]]
A classification of black holes by mass:
* [[Micro black hole]] and extra-dimensional black hole
* [[Planck length]]
* [[Primordial black hole]], a hypothetical leftover of the Big Bang
* [[Stellar black hole]], which could either be a static black hole or a rotating black hole
* [[Supermassive black hole]], which could also either be a static black hole or a rotating black hole
* [[Visible universe]], if its density is the [[Friedmann equations#Density parameter|critical density]], as a [[black hole cosmology|hypothetical black hole]]
* [[Virtual black hole]]

== References ==
{{reflist|30em}}

{{Black holes}}
{{authority control}}


[[Category:Black holes]]
[[Category:1916 in science]]
[[Category:Radii]]

Big Bounce

2025-10-31T16:36:33Z

2405:6E00:63A:E7E9:FC59:A773:B530:FF58:

{{Short description|Model for the origin of the universe}}
{{Other uses|The Big Bounce (disambiguation)}}
{{cosmology}}
[[File:Big Bounce.gif|thumb|An animation of the Big Bounce]]
The '''Big Bounce''' hypothesis is a [[cosmological model]] for the origin of the known [[universe]]. It was originally suggested as a phase of the ''[[cyclic model]]'' or ''oscillatory universe'' interpretation of the [[Big Bang]], where the first cosmological event was the result of the collapse of a previous universe.<ref>{{Cite journal |last1=Abelev |first1=B. |last2=Adam |first2=J. |last3=Adamová |first3=D. |last4=Aggarwal |first4=M. M. |last5=Aglieri Rinella |first5=G. |last6=Agnello |first6=M. |last7=Agostinelli |first7=A. |last8=Agrawal |first8=N. |last9=Ahammed |first9=Z. |last10=Ahmad |first10=N. |last11=Ahmed |first11=I. |last12=Ahn |first12=S. U. |last13=Ahn |first13=S. A. |last14=Aimo |first14=I. |last15=Aiola |first15=S. |date=2014-11-10 |title=Beauty production in pp collisions at s=2.76 TeV measured via semi-electronic decays |url=http://cds.cern.ch/record/1702572/files/scoap3-fulltext.pdf |journal=Physics Letters B |language=en |volume=738 |pages=97–108 |doi=10.1016/j.physletb.2014.09.026 |s2cid=119489459 |issn=0370-2693|doi-access=free }}</ref><ref>{{Cite journal |last1=Novello |first1=M. |last2=Bergliaffa |first2=S. E. Perez |date=2008-07-01 |title=Bouncing cosmologies |url=https://www.sciencedirect.com/science/article/pii/S0370157308001373 |journal=Physics Reports |language=en |volume=463 |issue=4 |pages=127–213 |doi=10.1016/j.physrep.2008.04.006 |arxiv=0802.1634 |bibcode=2008PhR...463..127N |s2cid=119274449 |issn=0370-1573}}</ref><ref>{{Cite journal |last1=Finelli |first1=Fabio |last2=Brandenberger |first2=Robert |date=2002-05-15 |title=Generation of a scale-invariant spectrum of adiabatic fluctuations in cosmological models with a contracting phase |url=https://link.aps.org/doi/10.1103/PhysRevD.65.103522 |journal=Physical Review D |volume=65 |issue=10 |article-number=103522 |doi=10.1103/PhysRevD.65.103522|arxiv=hep-th/0112249 |bibcode=2002PhRvD..65j3522F |s2cid=7262222 }}</ref><ref>{{Cite journal |last1=Ashtekar |first1=Abhay |last2=Pawlowski |first2=Tomasz |last3=Singh |first3=Parampreet |date=2 October 2006 |title=Quantum nature of the big bang: Improved dynamics |journal=Physical Review D |volume=74 |issue=8 |article-number=084003 |arxiv=gr-qc/0607039 |bibcode=2006PhRvD..74h4003A |doi=10.1103/PhysRevD.74.084003 |s2cid=34651070}}</ref> It receded from serious consideration in the early 1980s after [[Inflation (cosmology)|inflation theory]] emerged as a solution to the [[horizon problem]], which had arisen from advances in observations revealing the [[Observable universe#Large-scale structure|large-scale structure]] of the universe.

Inflation was found to be inevitably [[Eternal inflation|eternal]], creating an infinity of different universes with typically different properties, suggesting that the properties of the observable universe are a matter of chance.<ref name="Nautilus2014">{{cite news |last1=McKee |first1=Maggie |date=25 September 2014 |title=Ingenious: Paul J. Steinhardt – The Princeton physicist on what's wrong with inflation theory and his view of the Big Bang |work=Nautilus |publisher=NautilusThink Inc. |issue=17 |url=http://nautil.us/issue/17/big-bangs/ingenious-paul-j-steinhardt |access-date=31 March 2017 |archive-url=https://web.archive.org/web/20170123052634/http://nautil.us/issue/17/big-bangs/ingenious-paul-j-steinhardt |archive-date=23 January 2017 |ref=Chapter 4}}</ref> An alternative concept that included a Big Bounce was conceived as a predictive and falsifiable possible solution to the horizon problem.<ref name="SteinhardtTurok2005">{{cite journal |last1=Steinhardt |first1=Paul J. |last2=Turok |first2=Neil |year=2005 |title=The cyclic model simplified |journal=New Astronomy Reviews |volume=49 |issue=2–6 |pages=43–57 |arxiv=astro-ph/0404480 |bibcode=2005NewAR..49...43S |doi=10.1016/j.newar.2005.01.003 |issn=1387-6473 |s2cid=16034194}}</ref> Investigation continued as of 2022.<ref>{{Cite journal|title=Entropy, black holes, and the new cyclic universe|first1=Anna|last1=Ijjas|first2=Paul J.|last2=Steinhardt|date=January 10, 2022|journal=Physics Letters B|volume=824|article-number=136823|doi=10.1016/j.physletb.2021.136823|doi-access=free|arxiv=2108.07101|bibcode=2022PhLB..82436823I }}</ref><ref>{{Cite web|url=https://www.quantamagazine.org/big-bounce-simulations-challenge-the-big-bang-20200804/|title=Big Bounce Simulations Challenge the Big Bang|first=Charlie|last=Wood|date=August 4, 2020|website=Quanta Magazine}}</ref><ref name="LehnersSteinhardt2013">{{cite journal |last1=Lehners |first1=Jean-Luc |last2=Steinhardt |first2=Paul J. |year=2013 |title=Planck 2013 results support the cyclic universe |journal=Physical Review D |volume=87 |issue=12 |article-number=123533 |arxiv=1304.3122 |bibcode=2013PhRvD..87l3533L |doi=10.1103/PhysRevD.87.123533 |issn=1550-7998 |s2cid=76656473}}</ref><ref name="BrandenbergerPeter2017">{{cite journal |last1=Brandenberger |first1=Robert |last2=Peter |first2=Patrick |year=2017 |title=Bouncing Cosmologies: Progress and Problems |journal=Foundations of Physics |volume=47 |issue=6 |pages=797–850 |arxiv=1603.05834 |bibcode=2017FoPh...47..797B |doi=10.1007/s10701-016-0057-0 |issn=0015-9018 |s2cid=118847768}}</ref>

== Expansion and contraction ==
The concept of the Big Bounce envisions the Big Bang as the beginning of a [[metric expansion of space|period of expansion]] that followed a period of contraction.<ref>{{cite web |url=https://magazine.columbia.edu/article/was-big-bang-really-big-bounce |title=Was the Big Bang Really a Big Bounce? |last=Craig |first=David J. |year=2018 |website=Columbia Magazine |publisher=Columbia University |access-date=July 3, 2023}}</ref> In this view, one could talk of a "[[Big Crunch]]" followed by a "Big Bang" or, more simply, a "Big Bounce". This concept suggests that we could exist at any point in an infinite sequence of universes, or conversely, the current universe could be the very first iteration. However, if the condition of the interval phase "between bounces"—considered the "hypothesis of the primeval atom"—is taken into full contingency, such enumeration may be meaningless because that condition could represent a [[Gravitational singularity|singularity]] in time at each instance if such perpetual repeats (cycles) were absolute and undifferentiated.

The main idea behind the quantum theory of a Big Bounce is that, as density approaches infinity, the behavior of [[quantum foam]] changes. All the so-called [[dimensionless physical constant|fundamental physical constant]]s, including the speed of light in vacuum, need not remain constant during a Big Crunch, especially in the time interval smaller than that in which measurement may never be possible (one unit of [[Planck time]], roughly 10−43 seconds) spanning or bracketing the point of inflection.

== History ==
Big Bounce models were endorsed on largely aesthetic grounds by cosmologists including [[Willem de Sitter]], [[Carl Friedrich von Weizsäcker]], [[George C. McVittie|George McVittie]], and [[George Gamow]] (who stressed that "from the physical point of view we must forget entirely about the precollapse period").<ref>{{cite book |last=Kragh |first=Helge |url=https://archive.org/details/cosmologycontrov00helg |title=Cosmology |publisher=[[Princeton University Press]] |year=1996 |isbn=978-0-691-00546-1 |location=Princeton, New Jersey |language=en-us}}</ref>

By the early 1980s, the advancing precision and scope of [[observational cosmology]] had revealed that the [[Observable universe#Large-scale structure|large-scale structure]] of the universe is [[shape of the universe|flat]], [[wiktionary:homogeneous|homogeneous]], and [[isotropic]], a finding later accepted as the [[cosmological principle]] to apply at scales beyond roughly 300 million [[light-year]]s. This led cosmologists to seek an explanation to the [[horizon problem]], which questioned how distant regions of the universe could have identical properties without ever being in light-like communication. A solution was proposed to be a period of exponential expansion of space in the early universe, which formed the basis of what became known as [[Inflation (cosmology)|inflation theory]]. Following the brief inflationary period, the universe continues to expand at a slower rate.

Various formulations of inflation theory and their detailed implications became the subject of intense theoretical study. Without a compelling alternative, inflation became the leading solution to the horizon problem.

The phrase "Big Bounce" appeared in scientific literature in 1987, when it was first used in the title of a pair of articles (in German) in ''Stern und Weltraum'' by Wolfgang Priester and Hans-Joachim Blome.<ref>{{harvnb|Overduin|Blome|Hoell|2007}}</ref> It reappeared in 1988 in Iosif Rozental's ''Big Bang, Big Bounce'', a revised English-language translation of a Russian-language book (by a different title), and in a 1991 English-language article by Priester and Blome in ''Astronomy and Astrophysics''. The phrase originated as the title of [[The Big Bounce (novel)|a novel]] by [[Elmore Leonard]] in 1969, shortly after increased public awareness of the Big Bang model with of the discovery of the [[cosmic microwave background]] by [[Arno Penzias|Penzias]] and [[Robert Woodrow Wilson|Wilson]] in 1965.

The idea of the existence of a big bounce in the very early universe has found diverse support in works based on [[loop quantum gravity]]. In [[loop quantum cosmology]], a branch of loop quantum gravity, the big bounce was first discovered in February 2006 for isotropic and homogeneous models by [[Abhay Ashtekar]], [[Tomasz Pawlowski]], and [[Parampreet Singh]] at [[Pennsylvania State University]].<ref>{{Cite journal |last1=Ashtekar |first1=Abhay |last2=Pawlowski |first2=Tomasz |last3=Singh |first3=Parampreet |date=12 April 2006 |title=Quantum Nature of the Big Bang |journal=Physical Review Letters |language=en |volume=96 |issue=14 |article-number=141301 |arxiv=gr-qc/0602086 |bibcode=2006PhRvL..96n1301A |doi=10.1103/PhysRevLett.96.141301 |issn=0031-9007 |pmid=16712061 |s2cid=3082547 |ref={{harvid|Ashtekar et al.|2006}}}}</ref> This result has been generalized to various other models by different groups, and includes the case of spatial curvature, cosmological constant, anisotropies, and Fock quantized inhomogeneities.<ref>{{Cite journal|last1=Ashtekar|first1=Abhay|last2=Singh|first2=Parampreet|date=2011-11-07|title=Loop Quantum Cosmology: A Status Report|journal=Classical and Quantum Gravity|volume=28|issue=21|article-number=213001|doi=10.1088/0264-9381/28/21/213001|issn=0264-9381|arxiv=1108.0893|bibcode=2011CQGra..28u3001A|s2cid=119209230}}</ref>

[[Martin Bojowald]], an assistant professor of physics at Pennsylvania State University, published a study in July 2007 detailing work related to loop quantum gravity that claimed to mathematically solve the time before the Big Bang, which would give new weight to the oscillatory universe and Big Bounce theories.<ref name="Bojowald2007">{{cite journal |last=Bojowald |first=Martin |year=2007 |title=What happened before the Big Bang? |journal=Nature Physics |volume=3 |issue=8 |pages=523–525 |doi=10.1038/nphys654 |url= https://zenodo.org/record/896670|bibcode = 2007NatPh...3..523B |doi-access=free }}</ref>

One of the main problems with the Big Bang theory is that there is a [[Gravitational singularity|singularity]] of zero volume and infinite energy at the moment of the Big Bang. This is normally interpreted as a breakdown of physics as we know it; in this case, of the theory of [[general relativity]]. This is why one expects quantum effects to become important and avoid a singularity.

However, research in loop quantum cosmology purported to show that a previously existing universe collapses not to a singularity, but to a point where the quantum effects of gravity become so strongly repulsive that the universe rebounds back out, forming a new branch. Throughout this collapse and bounce, the evolution is unitary.

Bojowald also claimed that some properties of the universe that collapsed to form ours can be determined; however, other properties are not determinable due to some [[uncertainty principle]]. This result has been disputed by different groups, which show that due to restrictions on fluctuations stemming from the uncertainty principle, there are strong constraints on the change in relative fluctuations across the bounce.<ref>{{Cite journal|last1=Corichi|first1=Alejandro|last2=Singh|first2=Parampreet|date=2008-04-23|title=Quantum Bounce and Cosmic Recall|url=https://link.aps.org/doi/10.1103/PhysRevLett.100.161302|journal=Physical Review Letters|volume=100|issue=16|article-number=161302|doi=10.1103/PhysRevLett.100.161302|pmid=18518182|arxiv=0710.4543|bibcode=2008PhRvL.100p1302C|s2cid=40071231}}</ref><ref>{{Cite journal|last1=Kamiński|first1=Wojciech|last2=Pawłowski|first2=Tomasz|date=2010-04-15|title=Cosmic recall and the scattering picture of loop quantum cosmology|url=https://link.aps.org/doi/10.1103/PhysRevD.81.084027|journal=Physical Review D|volume=81|issue=8|article-number=084027|doi=10.1103/PhysRevD.81.084027|arxiv=1001.2663|bibcode=2010PhRvD..81h4027K|hdl=10261/66991 |s2cid=44771809}}</ref>

While the existence of the Big Bounce has still to be demonstrated from loop quantum gravity, the robustness of its main features has been confirmed using exact results<ref>{{Cite journal |last1=Ashtekar |first1=Abhay |last2=Corichi |first2=Alejandro |last3=Singh |first3=Parampreet |year=2008 |title=Robustness of key features of loop quantum cosmology |journal=Physical Review D |language=en |volume=77 |issue=2 |article-number=024046 |arxiv=0710.3565 |bibcode=2008PhRvD..77b4046A |doi=10.1103/PhysRevD.77.024046 |issn=1550-7998 |s2cid=118674251}}</ref> and several studies involving numerical simulations using [[High Performance Computing|high performance computing]] in loop quantum cosmology.

In 2006, it was proposed that the application of loop quantum gravity techniques to Big Bang cosmology can lead to a bounce that need not be cyclic.<ref>{{Cite news |date=May 17, 2006 |title=Penn State Researchers Look Beyond The Birth Of The Universe |url=https://www.sciencedaily.com/releases/2006/05/060515232747.htm |work=[[Science Daily]] |language=en}} Referring to {{harv|Ashtekar et al.|2006}}</ref>

In 2010, [[Roger Penrose]] advanced a general relativity-based theory which he called the "[[conformal cyclic cosmology]]". The theory explains that the universe will expand until all matter decays and ultimately turns to light. Since nothing in the universe would have any time or distance scale associated with it, the universe becomes identical with the Big Bang, resulting in a type of Big Crunch that becomes the next Big Bang, thus perpetuating the next cycle.<ref>{{Cite book |last=Penrose |first=Roger |author-link=Roger Penrose |title=Cycles of time: an extraordinary new view of the universe |title-link=Cycles of Time |date=2011 |publisher=Alfred A. Knopf |isbn=978-0-224-08036-1 |edition=1st |location=New York |oclc=676726661}}</ref>

In 2011, [[Nikodem Popławski]] showed that a nonsingular Big Bounce appears naturally in the [[Einstein–Cartan theory|Einstein–Cartan]]–Sciama–Kibble theory of gravity.<ref>{{Cite journal |last=Popławski |first=Nikodem |author-link=Nikodem Popławski |year=2012 |title=Nonsingular, big-bounce cosmology from spinor-torsion coupling |journal=Physical Review D |language=en |volume=85 |issue=10 |article-number=107502 |arxiv=1111.4595 |bibcode=2012PhRvD..85j7502P |doi=10.1103/PhysRevD.85.107502 |issn=1550-7998 |s2cid=118434253}}</ref> This theory extends general relativity by removing a constraint of the symmetry of the [[affine connection]] and regarding its antisymmetric part, the [[torsion tensor]], as a dynamical variable. The minimal coupling between torsion and Dirac [[Spinor|spinors]] generates a spin-spin interaction which is significant in fermionic matter at extremely high densities. Such an interaction avoids the unphysical Big Bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the universe was contracting. This scenario also explains why the present Universe at the largest scales appears spatially flat, homogeneous, and isotropic, providing a physical alternative to cosmic inflation.

In 2012, a new theory of a nonsingular Big Bounce was constructed within the frame of standard Einstein gravity.<ref>{{Cite journal |last1=Cai |first1=Yi-Fu |last2=Easson |first2=Damien A |last3=Brandenberger |first3=Robert |author-link3=Robert Brandenberger |year=2012 |title=Towards a nonsingular bouncing cosmology |journal=[[Journal of Cosmology and Astroparticle Physics]] |volume=2012 |issue=8 |page=020 |arxiv=1206.2382 |bibcode=2012JCAP...08..020C |doi=10.1088/1475-7516/2012/08/020 |issn=1475-7516 |s2cid=118679321}}</ref> This theory combines the benefits of matter bounce and [[ekpyrotic cosmology]]. Particularly, in the homogeneous and isotropic background cosmological solution, the [[BKL singularity|BKL instability]] is unstable to the growth of anisotropic stress, which is resolved in this theory. Moreover, curvature perturbations seeded in matter contraction can form a nearly scale-invariant primordial power spectrum and thus provide a consistent mechanism to explain the [[cosmic microwave background]] (CMB) observations.

A few sources argue that distant [[supermassive black holes]] whose large size is hard to explain so soon after the Big Bang, such as [[ULAS J1342+0928]],<ref name="NASA-20171206">{{cite web |last1=Landau |first1=Elizabeth |last2=Bañados |first2=Eduardo |title=Found: Most Distant Black Hole |url=https://www.jpl.nasa.gov/news/news.php?feature=7017 |date=6 December 2017 |work=[[NASA]] |access-date=6 December 2017 | quote="This black hole grew far larger than we expected in only 690 million years after the Big Bang, which challenges our theories about how black holes form," said study co-author Daniel Stern of NASA's Jet Propulsion Laboratory in Pasadena, California.}}</ref> may be evidence for a Big Bounce, with these supermassive black holes being formed before the Big Bounce.<ref name="News_com-AU_2017-12-07a">{{Cite web |last=Seidel |first=Jamie |date=7 December 2017 |title=Black hole at the dawn of time challenges our understanding of how the universe was formed |url=http://www.news.com.au/technology/science/space/black-hole-at-the-dawn-of-time-challenges-our-understanding-of-how-the-universe-was-formed/news-story/3279356705a47d45416ae2e6ead41175 |access-date=9 December 2017 |publisher=News Corp Australia |quote=It had reached its size just 690 million years after the point beyond which there is nothing. The most dominant scientific theory of recent years describes that point as the Big Bang—a spontaneous eruption of reality as we know it out of a quantum singularity. But another idea has recently been gaining weight: that the universe goes through periodic expansions and contractions—resulting in a "Big Bounce". Early black holes have been predicted to be a key telltale as to whether or not the idea may be valid. This one is very big. To get to its size—800 million times more mass than our Sun—it must have swallowed a lot of stuff. ... As far as we understand it, the universe wasn't old enough at that time to generate such a monster.}}</ref><ref name=YouMagazine2017-12-08a>{{cite web|url=http://www.youmagazine.gr/2017/12/23256-mia-mavri-trypa-arhaioteri-apo-to-sympan-video/|title=A Black Hole that is more ancient than the Universe|date=8 December 2017|access-date=9 December 2017|publisher=You Magazine (Greece)|language=el|quote=This new theory that accepts that the Universe is going through periodic expansions and contractions is called "Big Bounce"}}</ref>

==Critics==
According to a study published in [[Physical Review Letters]] in May 2023, the Big Bounce should have left marks in the primordial light, known as the [[cosmic microwave background]] (CMB), but comparing observations conducted by the [[Planck Surveyor|Planck satellite]] with the simulated CMB in the case the Universe bounced on itself only once, that particular bounce signature was not found.<ref>{{Cite journal |last1=van Tent |first1=Bartjan |last2=Delgado |first2=Paola C. M. |last3=Durrer |first3=Ruth |date=2023-05-09 |title=Constraining the Bispectrum from Bouncing Cosmologies with Planck |journal=Physical Review Letters |language=en |volume=130 |issue=19 |article-number=191002 |doi=10.1103/PhysRevLett.130.191002 |pmid=37243637 |arxiv=2212.05977 |bibcode=2023PhRvL.130s1002V |issn=0031-9007}}</ref>
==See also==
{{div col|colwidth=30em}}
* {{annotated link|Abhay Ashtekar}}
* {{annotated link|Anthropic principle}}
* {{annotated link|Big Crunch}}
* {{annotated link|Big Freeze}}
* {{annotated link|Big Rip}}
* {{annotated link|Black hole}}
* {{annotated link|Eternal return}}
* {{annotated link|False vacuum}}
* {{annotated link|John Archibald Wheeler}}
* {{annotated link|Loop quantum cosmology}}
* {{annotated link|Loop quantum gravity}}
* {{annotated link|Supernova}}
{{div col end}}

==References==
<references />

==Further reading==
* Angha, Nader (2001). ''Expansion & Contraction Within Being (Dahm).'' Riverside, California: M.T.O Shahmaghsoudi Publications. {{ISBN|0-910735-61-1}}.
* {{cite journal |last=Bojowald |first=Martin |year=2008|title=Follow the Bouncing Universe |journal=Scientific American |volume= 299|issue=October 2008 |pages=44–51| doi= 10.1038/scientificamerican1008-44|doi-broken-date=11 July 2025 |pmid=18847084|bibcode = 2008SciAm.299d..44B }}
* {{cite book |title=Faster than the Speed of Light: the Story of a Scientific Speculation |last=Magueijo |first=João |year=2003 |publisher=Perseus Publishing |location=Cambridge, Massachusetts |language=en-us |isbn=978-0-7382-0525-0 |url=https://archive.org/details/fasterthanspeedo00magu}}
* Taiebyzadeh, Payam (2017). ''String Theory; A unified theory and inner dimension of elementary particles (BazDahm).'' Riverside, Iran: Shamloo Publications Center. {{ISBN|978-600-116-684-6}}.

==External links==
* {{Cite journal |last1=Overduin |first1=James |last2=Blome |first2=Hans-Joachim |last3=Hoell |first3=Josef |year=2007 |title=Wolfgang Priester: From the big bounce to the λ-dominated universe |journal=Naturwissenschaften |volume=94 |issue=6 |pages=417–429 |arxiv=astro-ph/0608644 |bibcode=2007NW.....94..417O |doi=10.1007/s00114-006-0187-x |pmid=17146687 |s2cid=9204407}}
* {{cite arXiv |eprint=physics/9812021v2|last1=Pitts|first1=Trevor|title=Dark Matter, Antimatter and Time-Symmetry|year=1998 }}
* [https://web.archive.org/web/20100225174459/http://www.science.psu.edu/news-and-events/2006-news/Ashtekar5-2006.htm Penn State Researchers Look Beyond The Birth Of The Universe] (Penn State) May 12, 2006
* [https://web.archive.org/web/20101013152619/http://www.science.psu.edu/news-and-events/2007-news/Bojowald6-2007.htm What Happened Before the Big Bang?] (Penn State) July 1, 2007
* [http://gravity.psu.edu/outreach/articles/bigbounce.pdf From big bang to big bounce] (Penn State) NewScientist December 13, 2008
* {{Cite journal |last=Nurgaliev |first=I. S. |year=2010 |title=Singularities are averted by vortices |journal=Gravitation and Cosmology |language=en |volume=16 |issue=4 |pages=313–315 |bibcode=2010GrCo...16..313N |doi=10.1134/S0202289310040092 |issn=0202-2893 |s2cid=119982190}}

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[[Category:Physical cosmology]]
[[Category:Ultimate fate of the universe]]