Editing Black hole (section)

== Formation and evolution ==
Given the bizarre character of black holes, it was long questioned whether such objects could actually exist in nature or whether they were merely pathological solutions to Einstein's equations. Einstein himself wrongly thought black holes would not form, because he held that the angular momentum of collapsing particles would stabilise their motion at some radius.<ref>{{Cite journal |last=Einstein |first=A. |title=On A Stationary System With Spherical Symmetry Consisting of Many Gravitating Masses |journal=Annals of Mathematics |volume=40 |issue=4 |pages=922–936 |date=1939 |doi=10.2307/1968902 |bibcode=1939AnMat..40..922E|jstor=1968902|s2cid=55495712 |url=http://pdfs.semanticscholar.org/8dd0/dfafef0c53c428fdc3b58f8099aafcf7d089.pdf |archive-url=https://web.archive.org/web/20190228153449/http://pdfs.semanticscholar.org/8dd0/dfafef0c53c428fdc3b58f8099aafcf7d089.pdf |archive-date=28 February 2019 }}</ref> This led the general relativity community to dismiss all results to the contrary for many years. However, a minority of relativists continued to contend that black holes were physical objects,<ref>{{cite book |chapter=The Kerr and Kerr-Schild metrics |first=R. P. |last=Kerr |title=The Kerr Spacetime |editor1-first=D. L. |editor1-last=Wiltshire |editor2-first=M. |editor2-last=Visser |editor3-first=S. M. |editor3-last=Scott |publisher=Cambridge University Press |date=2009 |isbn=978-0-521-88512-6 |arxiv=0706.1109 |bibcode=2007arXiv0706.1109K}}</ref> and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to the formation of an event horizon.<ref>{{Cite web |last=Findley |first=Kate |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 |language=en-US }}</ref>

Penrose demonstrated that once an event horizon forms, general relativity without quantum mechanics requires that a singularity will form within.<ref name=penrose1965 /> Shortly afterwards, Hawking showed that many cosmological solutions that describe the [[Big Bang]] have singularities without [[scalar field]]s or other [[exotic matter]].{{clarify|date=February 2016}} The [[Kerr solution]], the no-hair theorem, and the laws of black hole thermodynamics showed that the physical properties of black holes were simple and comprehensible, making them respectable subjects for research.<ref name=HawkingPenrose1970>{{Cite journal |first1=S. W. |last1=Hawking |author-link1=Stephen Hawking |first2=R. |last2=Penrose |author-link2=Roger Penrose |title=The Singularities of Gravitational Collapse and Cosmology |journal=[[Proceedings of the Royal Society A]] |volume=314 |issue=1519 |pages=529–548 |date=January 1970 |doi=10.1098/rspa.1970.0021|jstor=2416467 |bibcode=1970RSPSA.314..529H|doi-access=free}}</ref> Conventional black holes are formed by [[gravitational collapse]] of heavy objects such as stars, but they can also in theory be formed by other processes.<ref name="pacucci2016" /><ref name="carr primordial" />

=== 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 news |title=Ripped Apart by a Black Hole |url=http://www.eso.org/public/news/eso1332/ |access-date=19 July 2013 |newspaper=ESO Press Release |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. For stars this usually occurs either because a star has too little "fuel" left to maintain its temperature through [[stellar nucleosynthesis]], or because a star that would have been stable receives extra matter in a way that does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight.<ref name="Carroll5.8">{{harvnb|Carroll|2004|loc=Section 5.8}}</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]]. The result is one of the various types of [[compact star]]. 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" />

If the mass of the remnant exceeds about {{Solar mass|3–4}} (the Tolman–Oppenheimer–Volkoff limit<ref name="OV1939" />), either because the original star was very heavy or because the remnant collected additional mass through accretion of matter, even the degeneracy pressure of [[neutron]]s is insufficient to stop the collapse. No known mechanism (except possibly quark degeneracy pressure) is powerful enough to stop the implosion and the object will inevitably collapse to form a black hole.<ref name="Carroll5.8" />

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. 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 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=Inflating Horizon of Particle Astrophysics and Cosmology |pages=astro–ph/0511743 |publisher=Universal Academy Press |date=2005 |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]] there was a net repulsive gravitation in the beginning until the end of inflation. Since then the [[Hubble flow]] was slowed by the energy density of the universe.

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 ===
Gravitational collapse is not the only process that could create black holes. In principle, black holes could be formed in [[high-energy physics|high-energy]] 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 |page=056010 |doi=10.1103/PhysRevD.65.056010 |arxiv=hep-ph/0106219|bibcode=2002PhRvD..65e6010G|s2cid=1203487 }}</ref> This suggests that there must be a lower limit for the mass of black holes. Theoretically, this boundary is expected to lie around the Planck mass, where quantum effects are expected to invalidate the predictions of general relativity.<ref>{{cite journal |last1=Harada |first1=T. |title=Is there a black hole minimum mass? |journal=Physical Review D |volume=74 |issue=8 |page=084004 |date=2006 |doi=10.1103/PhysRevD.74.084004 |arxiv=gr-qc/0609055 |bibcode=2006PhRvD..74h4004H |s2cid=119375284}}</ref>

This would put the creation of black holes firmly out of reach of any high-energy process occurring on or near the Earth. However, certain developments in quantum gravity suggest that the minimum black hole mass could be much lower: some [[braneworld]] scenarios for example put the boundary as low as {{val|1|u=TeV/c2}}.<ref>{{Cite journal |last1=Arkani–Hamed |first1=N. |last2=Dimopoulos |first2=S. |last3=Dvali |first3=G. |title=The hierarchy problem and new dimensions at a millimeter |journal=Physics Letters B |volume=429 |issue=3–4 |pages=263–272 |date=1998 |arxiv=hep-ph/9803315 |doi=10.1016/S0370-2693(98)00466-3|bibcode=1998PhLB..429..263A|s2cid=15903444 }}</ref> This would make it conceivable for [[micro black hole]]s to be 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]]. These theories are very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists.<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 |page=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>

=== 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. 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 |page=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 |page=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, however, 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> 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>

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 perhaps {{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>