You do not have permission to edit this page, for the following reasons:

This IP address has been blocked from editing Wikipedia.
This does not affect your ability to read Wikipedia pages.
Most people who see this message have done nothing wrong. Some kinds of blocks restrict editing from specific service providers or telecom companies in response to recent abuse or vandalism, and can sometimes affect other users who are unrelated to that abuse. Review the information below for assistance if you do not believe that you have done anything wrong.

The IP address or range 34.205.0.0/16 has been blocked (disabled) by ‪ST47‬ for the following reason(s):

The IP address that you are currently using has been blocked because it is believed to be a web host provider. To prevent abuse, web hosts may be blocked from editing Wikipedia.
You will not be able to edit Wikipedia using a web host provider because it hides your IP address, much like a proxy or VPN.
We recommend that you attempt to use another connection to edit. For example, if you use a proxy or VPN to connect to the internet, turn it off when editing Wikipedia. If you edit using a mobile connection, try using a Wi-Fi connection, and vice versa. If you are using a corporate internet connection, switch to a different Wi-Fi network. If you have a Wikipedia account, please log in.
If you do not have any other way to edit Wikipedia, you will need to request an IP block exemption.

How to appeal if you are confident that your connection does not use a web host's IP address:
If you are confident that you are not using a web host, you may appeal this block by adding the following text on your talk page: ((unblock|reason=Caught by a web host block but this host or IP is not a web host. My IP address is _______. Place any further information here. ~~~~)). You must fill in the blank with your IP address for this block to be investigated. Your IP address can be determined here. Alternatively, if you wish to keep your IP address private you can use the unblock ticket request system. There are several reasons you might be editing using the IP address of a web host (such as if you are using VPN software or a business network); please use this method of appeal only if you think your IP address is in fact not a web host.

Administrators: The IP block exemption user right should only be applied to allow users to edit using web host in exceptional circumstances, and they should usually be directed to the functionaries team via email. If you intend to give the IPBE user right, a CheckUser needs to take a look at the account. This can be requested most easily at SPI Quick Checkuser Requests. Unblocking an IP or IP range with this template is highly discouraged without at least contacting the blocking administrator.

This block will expire on 05:44, 30 September 2026.

Even when blocked, you will usually still be able to edit your user talk page, as well as email administrators and other editors.

For information on how to proceed, please read the FAQ for blocked users and the guideline on block appeals. The guide to appealing blocks may also be helpful.

Other useful links: Blocking policy · Help:I have been blocked
Your IP address is in a range that has been blocked on all Wikimedia Foundation wikis. The block was made by ‪Jon Kolbert‬. The reason given is Open proxy/Webhost: See the help page if you are affected .
- Start of block: 05:38, 21 February 2024
- Expiry of block: 05:38, 21 February 2029
Your current IP address is 34.205.141.108. The blocked range is 34.205.0.0/16. Please include all above details in any queries you make. If you believe you were blocked by mistake, you can find additional information and instructions in the No open proxies global policy. Otherwise, to discuss the block please post a request for review on Meta-Wiki. You could also send an email to the stewards VRT queue at stewards@wikimedia.org including all above details.

You can view and copy the source of this page:

((Short description|Thermal radiation believed to be emitted by black holes due to quantum effects))
((General relativity sidebar))

'''Hawking radiation''' is the theoretical thermal [[black-body radiation]] released outside a [[black hole]]'s [[event horizon]]. This is counterintuitive because once ordinary [[electromagnetic radiation]] is inside the event horizon, it cannot escape. It is named after the physicist [[Stephen Hawking]], who developed a theoretical argument for its existence in 1974.<ref>((cite web |url-status=dead |url=http://www.charlierose.com/guest/view/6294 |archive-url=https://web.archive.org/web/20130329060031/http://www.charlierose.com/guest/view/6294 |archive-date=March 29, 2013 |first=Charlie |last=Rose |title=A conversation with Dr. Stephen Hawking & Lucy Hawking |website=charlierose.com ))</ref> Hawking radiation is predicted to be extremely faint and is many orders of magnitude below the current best telescopes' detecting ability.

Hawking radiation reduces the mass and rotational energy of black holes and is therefore also theorized to cause black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish.

For all except the smallest black holes, this happens extremely slowly. The radiation temperature is inversely proportional to the black hole's mass, so [[micro black hole]]s are predicted to be larger emitters of radiation than larger black holes and should dissipate faster per their mass. As such, if small black holes exist such as permitted by the hypothesis of [[primordial black holes]], they ought to die the fastest the smaller they shrink, leading to a final cataclysm of high energy radiation alone.<ref name="hawking-1974">((Cite journal|last=Hawking|first=S. W.|date=1974-03-01|title=Black hole explosions?|journal=Nature|language=en|volume=248|issue=5443|pages=30–31|doi=10.1038/248030a0|bibcode=1974Natur.248...30H|s2cid=4290107|issn=1476-4687))</ref> Such radiation bursts have not yet been detected.

== Overview ==
((more citations needed section|date = May 2023))
First predicted by [[Einstein]]'s 1915 theory of [[general relativity]], evidence for the astrophysical objects termed [[black holes]] began to mount half a century later,((citation needed|date = May 2023)) and these objects are of current interest primarily because of their compact size and immense [[gravitational attraction]].

A black hole can form when enough [[matter]] or [[energy]] is compressed into a volume small enough that the escape velocity is greater than the speed of light. Nothing can travel that fast, so nothing within a certain distance, proportional to the mass of the black hole, can escape beyond that distance. The region beyond which not even light can escape is the [[event horizon]]; an observer outside it cannot observe, become aware of, or be affected by events within the event horizon.((rp|25–36))

[[File:Andrew Hamilton schwarzchild waterfall.gif|thumb|Picture of space [[Gullstrand–Painlevé coordinates|infalling into a Schwarzschild black hole at the Newtonian escape speed]]. Outside/inside the horizon (red), the infalling speed is less/greater than the speed of light. At the event horizon, the infalling speed equals the speed of light.<ref name="hamilton" /> ''Credit'': Andrew Hamilton, JILA]]
Alternatively, using a set of [[Gullstrand–Painlevé coordinates|infalling coordinates]] in general relativity, one can conceptualize the event horizon as the region beyond which space is infalling faster than the speed of light. (Although nothing can travel ''through'' space faster than light, space itself can infall at any speed.)<ref name="hamilton">((cite web |last1=Hamilton |first1=Andrew |title=A Black Hole is a Waterfall of Space |url=https://jila.colorado.edu/~ajsh/insidebh/waterfall.html |website=jila.colorado.edu |access-date=1 September 2021 |quote=Physically, the Gullstrand–Painlevé metric describes space falling into the Schwarzschild black hole at the Newtonian escape velocity. ... At the horizon, the velocity equals the speed of light.))</ref> Once matter is inside the event horizon, all of the matter inside falls inevitably into a [[gravitational singularity]], a place of infinite curvature and zero size, leaving behind a warped spacetime devoid of any matter;((verify source|date = May 2023)) a classical black hole is pure empty [[spacetime]], and the simplest (nonrotating and uncharged) is characterized just by its mass and event horizon.<ref name="Levin 2021">((cite book |last1=Levin |first1=Janna |title=Black hole survival guide |date=2020 |publisher=Alfred A. Knopf, Penguin Random House |location=New York |isbn=9780525658221))</ref>((rp|37–43))

Our current understanding of quantum physics can be used to investigate what may happen in the region around the event horizon.((citation needed|date = May 2023)) In 1974, [[British people|British]] physicist [[Stephen Hawking]] used [[quantum field theory in curved spacetime]] to show that in theory, instead of cancelling each other out normally, the antimatter and matter fields were disrupted by the black hole, causing antimatter and matter particles to "blip" into existence as a result of the imbalanced matter fields, and drawing energy from the disruptor itself: the black holes (to escape), effectively draining energy from the black hole. In addition, not all of the particles were close to the event horizon, and the ones that were, could not escape. In effect this energy acted as if the black hole itself was slowly [[evaporation|evaporating]] (although it actually came from outside it).<ref>L. Susskind and J. Lindesay, ''An Introduction to Black Holes. Information and the String Theory Revolution'', World Scientific (2005). The tunneling process is described on pp.26–28, and described as Black Hole Evaporation on pp.48–49.</ref>((update after|2023|5|12))

However, according to the conjectured gauge-gravity duality (also known as the [[AdS/CFT correspondence]]), black holes in certain cases (and perhaps in general) are equivalent to solutions of [[quantum field theory]] at a non-zero [[temperature]]. This means that no information loss is expected in black holes (since the theory permits no such loss) and the radiation emitted by a black hole is probably the usual thermal radiation.((citation needed|date = May 2023)) If this is correct, then Hawking's original calculation should be corrected, though it is not known how (see [[#Trans-Planckian problem|below]]).

A black hole of one [[solar mass]] (((Solar mass|link=y))) has a temperature of only 60&nbsp;nanokelvins (60 [[Nano-|billionths]] of a [[kelvin]]); in fact, such a black hole would absorb far more [[cosmic microwave background radiation]] than it emits.((citation needed|date = May 2023)) A black hole of ((val|4.5|e=22|u=kg)) (about the mass of the [[Moon]], or about ((val|133|ul=um)) across) would be in equilibrium at 2.7&nbsp;K, absorbing as much radiation as it emits.((Citation needed|date=September 2020))

== Formulation ==
In 1972, [[Jacob Bekenstein]] developed a theory and reported that the black holes should have an entropy.<ref>((Cite journal |last1 = Bekenstein |first1 = A. |title =  Black holes and the second law |journal =  Lettere al Nuovo Cimento |volume = 4 |pages = 99–104 |year = 1972 |issue = 15 |doi = 10.1007/BF02757029 |s2cid = 120254309 ))</ref><ref>In the same year, he proposed his [[no-hair theorem]]s.((citation needed|date = May 2023))</ref> Bekenstein's theory and report came to [[Stephen Hawking]]'s attention,((clarify|date = May 2023))<!--The woord "commended" was removed, as it lacks citation support. In my understanding, Hawking was initially resistant, and only later took up an investigation himself. Find and read the history, this was not accurate as it stood.--> leading him to think about radiation due to this formalism.((citation needed|date = May 2023)) Hawking's subsequent theory and report followed a visit to Moscow in 1973, where Soviet scientists [[Yakov Zeldovich]] and [[Alexei Starobinsky]] convinced him that [[rotating black hole]]s ought to create and emit particles. Even still, Russian physicist [[Vladimir Gribov]] believed that even a non-rotating black hole should emit radiation. Hawking would find aspects of both of these arguments true once he did the calculation himself.<ref>((cite book |last1=Hawking |first1=Stephen |author-link=Stephen Hawking |title=A Brief History of Time |date=1988 |publisher=Bantam Books |isbn=0-553-38016-8 |title-link=A Brief History of Time))</ref>

According to the physicist [[Dmitri Diakonov]], there was an argument between Zeldovich and [[Vladimir Gribov]] at the Zeldovich Moscow 1972–1973 seminar. Zeldovich believed that only a rotating black hole could emit radiation, while Gribov believed that even a non-rotating black hole emits radiation due to the laws of quantum mechanics.<ref>((Cite web |url=http://scientific.ru/dforum/scilife/1318072669 |title=Memories of Dmitri Diakonov: "Грибов, Зельдович, Хокинг" |access-date=2015-09-24 |archive-date=2015-09-24 |archive-url=https://web.archive.org/web/20150924095313/http://scientific.ru/dforum/scilife/1318072669 |url-status=live ))</ref><ref>[https://web.archive.org/web/20220308165607/https://groups.google.com/g/fido7.ru.science/c/XYFuzxZyxmk?pli=1 Memories of Dmitri Diakonov: "Грибов, Зельдович, Хокинг"].</ref> This account is confirmed by Gribov's obituary in the [[Physics-Uspekhi]] by [[Vitaly Ginzburg]] and others.<ref>Vitaly Ginzburg et al., [http://93.175.29.54/book/s/00078786000872e8594c1de7a29bf0ea/Anselm-AA-UFN-1998-0 "Vladimir Gribov: obituary"]((Dead link|date=December 2022 |bot=InternetArchiveBot |fix-attempted=yes )).</ref><ref>Vitaly Ginzburg et al., [https://ufn.ru/ru/articles/1998/4/f/ "Vladimir Gribov: obituary"] (А. А. Ансельм, В. Л. Гинзбург, Ю. Л. Докшицер, И. Т. Дятлов, В. Е. Захаров, Б. Л. Иоффе, Л. Н. Липатов, Н. Н. Николаев, Л. Б. Окунь, Ю. В. Петров, К. А. Тер-Мартиросян, И. М. Халатников, "Памяти Владимира Наумовича Грибова").</ref>

==Emission process==
Hawking radiation is dependent on the [[Unruh effect]] and the [[equivalence principle]] applied to black-hole horizons. Close to the event horizon of a black hole, a local observer must accelerate to keep from falling in. An accelerating observer sees a thermal bath of particles that pop out of the local acceleration horizon, turn around, and free-fall back in. The condition of local thermal equilibrium implies that the consistent extension of this local thermal bath has a finite temperature at infinity, which implies that some of these particles emitted by the horizon are not reabsorbed and become outgoing Hawking radiation.<ref name="witt-blah" /><ref name="gubser pretorius">For an accessible discussion of the Unruh effect and Hawking radiation, see: ((cite book |last1=Gubser |first1=Steven S. |last2=Pretorius |first2=Frans |title=The little book of Black Holes |date=2017 |publisher=Princeton University Press |location=Princeton, New Jersey |isbn=978-0691163727 |pages=154–162 ))</ref>

A [[Schwarzschild black hole]] has a metric
: <math>(\mathrm{d}s)^2 = -\left(1 - \frac{2M}{r}\right)\,(\mathrm{d}t)^2 + \frac{1}{\left(1 - \frac{2M}{r}\right)} \,(\mathrm{d}r)^2 + r^2\,(\mathrm{d}\Omega)^2.</math>

The black hole is the background spacetime for a quantum field theory.

The field theory is defined by a local path integral, so if the boundary conditions at the horizon are determined, the state of the field outside will be specified. To find the appropriate boundary conditions, consider a stationary observer just outside the horizon at position
: <math>r = 2M + \frac{\rho^2}{8M}.</math>

The local metric to lowest order is
: <math>(\mathrm{d}s)^2 = -\left(\frac{\rho}{4M}\right)^2 \,(\mathrm{d}t)^2 + (\mathrm{d}\rho)^2 + (\mathrm{d}X_\perp)^2 = -\rho^2 \,(\mathrm{d}\tau)^2 + (\mathrm{d}\rho)^2 + (\mathrm{d}X_\perp)^2,</math>
which is [[Rindler coordinates|Rindler]] in terms of ((math|''τ'' ((=)) ((sfrac|''t''|4''M'')))). The metric describes a frame that is accelerating to keep from falling into the black hole. The local acceleration, ((math|''α'' ((=)) ((sfrac|1|''ρ'')))), diverges as ((math|''ρ'' → 0)).

The horizon is not a special boundary, and objects can fall in. So the local observer should feel accelerated in ordinary Minkowski space by the principle of equivalence. The near-horizon observer must see the field excited at a local temperature
: <math>T = \frac{\alpha}{2\pi} = \frac{1}{2\pi\rho} = \frac{1}{4\pi\sqrt{2Mr\left(1 - \frac{2M}{r}\right))),</math>
which is the [[Unruh effect]].

The gravitational redshift is given by the square root of the time component of the metric. So for the field theory state to consistently extend, there must be a thermal background everywhere with the local temperature redshift-matched to the near horizon temperature:

: <math>T(r') = \frac{1}{4\pi\sqrt{2Mr\left(1 - \frac{2M}{r}\right))) \sqrt\frac{1 - \frac{2M}{r)){1 - \frac{2M}{r')) = \frac{1}{4\pi\sqrt{2Mr\left(1 - \frac{2M}{r'}\right))).</math>

The inverse temperature redshifted to ((mvar|r′)) at infinity is

: <math>T(\infty) = \frac{1}{4 \pi \sqrt{2 M r)),</math>

and ((mvar|r)) is the near-horizon position, near ((math|2''M'')), so this is really

: <math>T(\infty) = \frac{1}{8 \pi M}.</math>

Thus a field theory defined on a black-hole background is in a thermal state whose temperature at infinity is

: <math>T_\text{H} = \frac{1}{8 \pi M}.</math>

From the black-hole temperature, it is straightforward to calculate the black-hole entropy ((mvar|S)). The change in entropy when a quantity of heat ((mvar|dQ)) is added is

: <math>\mathrm{d}S = \frac{\mathrm{d}Q}{T} = 8 \pi M \,\mathrm{d}Q.</math>

The heat energy that enters serves to increase the total mass, so

: <math>\mathrm{d}S = 8 \pi M \,\mathrm{d}M = \mathrm{d}(4 \pi M^2).</math>

The radius of a black hole is twice its mass in [[Planck units]], so the entropy of a black hole is proportional to its surface area:

: <math>S = \pi R^2 = \frac{A}{4}.</math>

Assuming that a small black hole has zero entropy, the integration constant is zero. Forming a black hole is the most efficient way to compress mass into a region, and this entropy is also a bound on the information content of any sphere in space time. The form of the result strongly suggests that the physical description of a gravitating theory can be [[holographic principle|somehow encoded]] onto a bounding surface.

==Black hole evaporation==
When particles escape, the black hole loses a small amount of its energy and therefore some of its mass (mass and energy are related by [[special relativity|Einstein's equation]] ((math|[[E = mc²|''E'' ((=)) ''mc''<sup>2</sup>]]))). Consequently, an evaporating black hole will have a finite lifespan. By [[dimensional analysis]], the life span of a black hole can be shown to scale as the cube of its initial mass,<ref name="page1976"/><ref name="wald1994">((cite book|last=Wald |first=Robert M. |author-link=Robert Wald |title=Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics |year=1994 |publisher=University of Chicago Press|isbn=9780226870250 |oclc=832158297))</ref>((rp|176–177)) and Hawking estimated that any black hole formed in the early universe with a mass of less than approximately 10<sup>12</sup>&nbsp;kg would have evaporated completely by the present day.<ref>((cite journal|first=S. W. |last=Hawking |title=Particle creation by black holes |doi=10.1007/BF02345020 |journal=[[Communications in Mathematical Physics]] |year=1975 |volume=43 |issue=3 |pages=199–220|bibcode=1975CMaPh..43..199H |s2cid=55539246 |url=http://projecteuclid.org/euclid.cmp/1103899181 ))</ref>

In 1976, [[Don Page (physicist)|Don Page]] refined this estimate by calculating the power produced, and the time to evaporation, for a non-rotating, non-charged [[Schwarzschild black hole]] of mass ((mvar|M)).<ref name="page1976">((cite journal |last=Page |first=Don N. |author-link=Don Page (physicist) |date=1976 |title=Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole |journal=[[Physical Review D]]|volume=13 |issue=2 |pages=198–206 |doi=10.1103/PhysRevD.13.198 |bibcode = 1976PhRvD..13..198P ))</ref> The time for the event horizon or entropy of a black hole to halve is known as the Page time.<ref name="don-page-bh-info">((cite journal | volume=71 | last = Page | first = Don N. | title = Information in Black Hole Radiation | journal = Physical Review Letters | pages = 3743–3746 | date = 6 December 1993 | issue = 23 | doi=10.1103/PhysRevLett.71.3743 | arxiv=hep-th/9306083 |bibcode = 1993PhRvL..71.3743P | pmid = 10055062 | s2cid = 9363821 ))</ref>  The calculations are complicated by the fact that a black hole, being of finite size, is not a perfect black body; the [[absorption cross section]] goes down in a complicated, [[Spin (physics)|spin]]-dependent manner as frequency decreases, especially when the wavelength becomes comparable to the size of the event horizon. Page concluded that primordial black holes could survive to the present day only if their initial mass were roughly ((val|4|e=11|u=kg)) or larger. Writing in 1976, Page using the understanding of neutrinos at the time erroneously worked on the assumption that neutrinos have no mass and that only two neutrino flavors exist, and therefore his results of black hole lifetimes do not match the modern results which take into account [[Neutrino#Flavor, mass, and their mixing|3 flavors of neutrinos with nonzero masses]]. A 2008 calculation using the particle content of the [[Standard Model]] and the [[Wilkinson Microwave Anisotropy Probe|WMAP]] figure for the age of the universe yielded a mass bound of ((val|5.00|0.04|e=11|u=kg)).<ref>((cite journal|arxiv=0709.2380 |title=Do Evaporating Black Holes Form Photospheres? |first1=Jane H. |last1=MacGibbon |first2=B. J. |last2=Carr |first3=Don N. |last3=Page |journal=[[Physical Review D]] |volume=78 |year=2008 |issue=6 |pages=064043 |doi=10.1103/PhysRevD.78.064043 |bibcode=2008PhRvD..78f4043M|s2cid=119230843 ))</ref>

Some pre-1998 calculations, using outdated assumptions about neutrinos, were as follows: If black holes evaporate under Hawking radiation, a solar mass black hole will evaporate over 10<sup>64</sup> years which is vastly longer than the age of the universe.<ref name="Frautschi">See page 596: table 1 and the "black hole decay" section and previous sentence on that page in  ((cite journal |doi=10.1126/science.217.4560.593 |pmid=17817517|quote=Since we have assumed a maximum scale of gravitational binding – for instance, superclusters of galaxies – black hole formation eventually comes to an end in our model, with masses of up to 10<sup>14</sup>((solar mass)) ... the timescale for black holes to radiate away all their energy ranges from to 10<sup>64</sup> years for black holes of one solar mass ...|title=Entropy in an Expanding Universe|journal=[[Science (journal)|Science]]|volume=217|issue=4560|pages=593–599|year=1982|last1=Frautschi|first1=Steven|bibcode=1982Sci...217..593F|s2cid=27717447))</ref> A supermassive black hole with a mass of 10<sup>11</sup> (100 billion) ((Solar mass|)) will evaporate in around ((val|2|e=100|u=years)).<ref name=page>((cite journal |doi=10.1103/PhysRevD.13.198|title=Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole|journal=[[Physical Review D]]|volume=13|issue=2|pages=198–206|year=1976|last1=Page|first1=Don N.|bibcode=1976PhRvD..13..198P)) See in particular equation (27).</ref> Some monster black holes in the universe are predicted to continue to grow up to perhaps 10<sup>14</sup> ((solar mass)) during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 2 × 10<sup>106</sup> years.<ref name="Frautschi"/> Post-1998 science modifies these results slightly; for example, the modern estimate of a solar-mass black hole lifetime is 10<sup>67</sup> years.<ref>((cite web |title=Ask Ethan: How Do Black Holes Actually Evaporate? |url=https://www.forbes.com/sites/startswithabang/2018/11/03/ask-ethan-how-do-black-holes-actually-evaporate/?sh=419e616024a1 |website=[[Starts With a Bang]] |publisher=[[Ethan Siegel]] |access-date=21 June 2023 |date=2018))</ref>

The [[Power (physics)|power]] emitted by a black hole in the form of Hawking radiation can be estimated for the simplest case of a nonrotating, non-charged [[Schwarzschild black hole]] of mass ((mvar|M)). Combining the formulas for the [[Schwarzschild radius]] of the black hole, the [[Stefan–Boltzmann law]] of blackbody radiation, the above formula for the temperature of the radiation, and the formula for the surface area of a [[sphere]] (the black hole's event horizon), several equations can be derived.

The Hawking radiation temperature is:<ref name="hawking-1974" /><ref name="hawking-radiation-calculator">[https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator Hawking Radiation Calculator]</ref><ref name="lopresto-bh-thermodynamics">((cite journal
| last = Lopresto
| first = Michael
| date = May 2003
| title = Some Simple Black Hole Thermodynamics
| url = https://web.stanford.edu/~oas/SI/SRGR/lib/BlackHoleThermoShort.pdf
| journal = The Physics Teacher
| volume = 41
| issue = 5
| pages = 299–301
| doi = 10.1119/1.1571268
| bibcode = 2003PhTea..41..299L
))</ref>

:<math>T_\mathrm{H} = \frac{\hbar c^3}{8 \pi G M k_\mathrm{B)) </math>

The Bekenstein–Hawking luminosity of a black hole, under the assumption of pure photon emission (i.e. that no other particles are emitted) and under the assumption that the horizon is the radiating surface is:<ref name="lopresto-bh-thermodynamics" /><ref name="hawking-radiation-calculator" />

:<math>P = \frac{\hbar c^6}{15360 \pi G^2 M^2} </math>

where ((mvar|P)) is the luminosity, i.e., the radiated power, ((mvar|ħ)) is the [[reduced Planck constant]], ((mvar|c)) is the [[speed of light]], ((mvar|G)) is the [[gravitational constant]] and ((mvar|M)) is the mass of the black hole. It is worth mentioning that the above formula has not yet been derived in the framework of [[semiclassical gravity]].

The time that the black hole takes to dissipate is:<ref name="lopresto-bh-thermodynamics" /><ref name="hawking-radiation-calculator" />

:<math>t_\mathrm{ev} = \frac{5120 \pi G^2 M^3}{\hbar c^4} = \frac{480 c^2 V}{\hbar G} \approx 3.396 \times 10^{-16} \, \mathrm{s} \  \left( {M \over \mathrm{kg)) \right)^3 \approx 2.140\times10^{67}\,\text{years} \ \left(\frac{M}{M_\odot}\right)^3,</math>

where ((math|''M'')) and ((math|''V'')) are the mass and (Schwarzschild) volume of the black hole. A black hole of one [[solar mass]] (((math|((solar mass)))) = ((val|2.0|e=30|u=kg))) takes more than ((val|e=67|u=years)) to evaporate—much longer than the current [[age of the universe]] at ((val|1.4|e=10|u=years)).<ref name="Planck 2015">((cite journal |author=Planck Collaboration |date=2016 |title=Planck 2015 results: XIII. Cosmological parameters |url=https://www.research.manchester.ac.uk/portal/files/52915797/aa25830_15.pdf |journal=[[Astronomy & Astrophysics|Astron. Astrophys.]] |volume=594 |at=A13, p. 31, Table 4 |arxiv=1502.01589 |bibcode=2016A&A...594A..13P |doi=10.1051/0004-6361/201525830 |hdl=10261/140585 |s2cid=119262962 |via=The University of Manchester's Research Explorer |access-date=27 October 2019))</ref> But for a black hole of ((val|e=11|u=kg)), the evaporation time is ((val|2.6|e=9|u=years)). This is why some astronomers are searching for signs of exploding [[primordial black holes]].

However, since the universe contains the [[cosmic microwave background radiation]], in order for the black hole to dissipate, the black hole must have a temperature greater than that of the present-day blackbody radiation of the universe of 2.7&nbsp;K. A study suggests that ((mvar|M)) must be less than 0.8% of the mass of the [[Earth]]<ref>((cite arXiv |last=Kapusta |first=Joseph |date=1999 |eprint=astro-ph/9911309 |title=The Last Eight Minutes of a Primordial Black Hole))</ref> – approximately the mass of the Moon.

It is also worth mentioning that quantum gravity effects are expected to modify the above formula for the black hole lifetime.<ref>((cite journal |last1=Campos Delgado|first1=Ruben |title=Quantum gravitational corrected evolution equations of charged black holes |journal=Journal of Holography Applications in Physics|year=2023 |volume=3 |issue=1 |pages=39–46|doi=10.22128/JHAP.2023.643.1037|s2cid=256868891 ))</ref>

Black hole evaporation has several significant consequences:
* Black hole evaporation produces a more consistent view of [[black hole thermodynamics]] by showing how black holes interact thermally with the rest of the universe.
* Unlike most objects, a black hole's temperature increases as it radiates away mass. The rate of temperature increase is exponential, with the most likely endpoint being the dissolution of the black hole in a violent burst of [[gamma ray]]s. A complete description of this dissolution requires a model of [[quantum gravity]], however, as it occurs when the black hole's mass approaches 1 [[Planck mass]], its radius will also approach two [[Planck length]]s.
* The simplest models of black hole evaporation lead to the [[black hole information paradox]]. The information content of a black hole appears to be lost when it dissipates, as under these models the Hawking radiation is random (it has no relation to the original information). A number of solutions to this problem have been proposed, including suggestions that Hawking radiation is perturbed to contain the missing information, that the Hawking evaporation leaves some form of remnant particle containing the missing information, and that information is allowed to be lost under these conditions.

== Problems and extensions ==
=== Quantum gravitational corrections ===
The Hawking formula of the black hole temperature is actually incomplete, because it does not take into account quantum gravity effects. In fact, one can treat general relativity as an effective field theory, i.e. one can view the [[Einstein–Hilbert action]] as the first term of a curvature expansion:<ref>((cite journal |last1=Barvinsky, Vilkovisky |first1=A.O, G.A |title=The generalized Schwinger-DeWitt technique and the unique effective action in quantum gravity |journal=Phys. Lett. B |year=1983 |volume=131 |issue=4–6 |pages=313–318 |doi=10.1016/0370-2693(83)90506-3 |bibcode=1983PhLB..131..313B ))</ref><ref>((cite journal |last1=Barvinsky, Vilkovisky |first1=A.O, G.A |title=The Generalized Schwinger-DeWitt Technique in Gauge Theories and Quantum Gravity |journal=Phys. Rep. |year=1985 |volume=119 |issue=1 |pages=1–74 |doi=10.1016/0370-1573(85)90148-6 |bibcode=1985PhR...119....1B ))</ref><ref>((cite journal |last1=Barvinsky, Vilkovisky |first1=A.O, G.A |title=Beyond the Schwinger-Dewitt Technique: Converting Loops Into Trees and In-In Currents |journal=Nucl. Phys. B|year=1987 |volume=282 |pages=163–188|doi=10.1016/0550-3213(87)90681-X |bibcode=1987NuPhB.282..163B ))</ref><ref>((cite journal |last1=Barvinsky, Vilkovisky |first1=A.O, G.A |title=Covariant perturbation theory. 2: Second order in the curvature. General algorithms |journal=Nucl. Phys. B|year=1990 |volume=333 |issue=2 |pages=471–511|doi=10.1016/0550-3213(90)90047-H |bibcode=1990NuPhB.333..471B ))</ref>

:<math> \begin{align}
\Gamma&=\int d^4x\, \sqrt{-g}\,\bigg(\frac{R}{16\pi G}+c_1(\mu)R^2
    +c_2(\mu)R_{\mu\nu}R^{\mu\nu}
    +c_3(\mu)R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\bigg)\\&-\int d^4 x \sqrt{-g}\bigg[\alpha R\ln\left(\frac{\Box}{\mu^2}\right)R
    +\beta R_{\mu\nu}\ln\left(\frac{\Box}{\mu^2}\right)R^{\mu\nu} + \gamma R_{\mu\nu\rho\sigma}\ln\left(\frac{\Box}{\mu^2}\right)R^{\mu\nu\rho\sigma}\bigg],
\end{align}</math>

where <math>\mu</math> is an arbitrary energy scale. The equations of motion derived from this effective action ultimately lead to a modification of the Hawking formula. For example, the temperature of a charged black hole was computed by Campos Delgado (using <math>k_\mathrm{B}=\hbar=c=1</math>) as<ref>((cite journal |last1=Campos Delgado|first1=Ruben |title=Quantum gravitational corrections to the entropy of a Reissner-Nordström black hole |journal=Eur. Phys. J. C|year=2022 |volume=82 |issue=3 |page=272 |doi=10.1140/epjc/s10052-022-10232-0|arxiv=2201.08293 |bibcode=2022EPJC...82..272C |s2cid=247824137 |doi-access=free ))</ref>

:<math> 
 T_H=\frac{1}{8\pi G M}
    +\frac{Q^2}{4G^3 M^5}\Big[2(c_2+4c_3)+\beta\left(4\gamma_E-9\right)+4\gamma\left(4\gamma_E-9\right)
    +4\left(\beta+4\gamma\right)\ln\left(2G M\mu\right)\Big]+\mathcal{O}\left(Q^4\right).
</math>

=== Trans-Planckian problem ===

The [[trans-Planckian problem]] is the issue that Hawking's original calculation includes [[quantum]] particles where the [[wavelength]] becomes shorter than the [[Planck length]] near the black hole's horizon. This is due to the peculiar behavior there, where time stops as measured from far away. A particle emitted from a black hole with a [[Wikt:finite|finite]] [[frequency]], if traced back to the horizon, must have had an [[Infinity|infinite]] frequency, and therefore a trans-Planckian wavelength.

The [[Unruh effect]] and the Hawking effect both talk about field modes in the superficially stationary [[spacetime]] that change frequency relative to other coordinates that are regular across the horizon. This is necessarily so, since to stay outside a horizon requires acceleration that constantly [[Doppler shift]]s the modes.((Citation needed|date=September 2020))

An outgoing [[photon]] of Hawking radiation, if the mode is traced back in time, has a frequency that diverges from that which it has at great distance, as it gets closer to the horizon, which requires the wavelength of the photon to "scrunch up" infinitely at the horizon of the black hole. In a maximally extended external [[Schwarzschild metric|Schwarzschild solution]], that photon's frequency stays regular only if the mode is extended back into the past region where no observer can go. That region seems to be unobservable and is physically suspect, so Hawking used a black hole solution without a past region that forms at a finite time in the past. In that case, the source of all the outgoing photons can be identified: a microscopic point right at the moment that the black hole first formed.

The quantum fluctuations at that tiny point, in Hawking's original calculation, contain all the outgoing radiation. The modes that eventually contain the outgoing radiation at long times are redshifted by such a huge amount by their long sojourn next to the event horizon that they start off as modes with a wavelength much shorter than the Planck length. Since the laws of physics at such short distances are unknown, some find Hawking's original calculation unconvincing.<ref>((Cite journal | doi = 10.1088/0034-4885/66/6/202|arxiv=gr-qc/0304042| title = Do black holes radiate?| journal =[[Reports on Progress in Physics]]| volume = 66| issue = 6| pages = 943–1008| year = 2003| last1 = Helfer | first1 = Adam D. |bibcode=2003RPPh...66..943H|s2cid=16668175))</ref><ref>((Cite journal |last1='t Hooft |first1=Gerard |author-link1=Gerard 't Hooft |doi=10.1016/0550-3213(85)90418-3 |title=On the quantum structure of a black hole |journal=[[Nuclear Physics B]] |volume=256 |pages=727–745 |year=1985 |bibcode=1985NuPhB.256..727T ))</ref><ref>((Cite journal | doi = 10.1103/PhysRevD.44.1731| pmid = 10014053| title = Black-hole evaporation and ultrashort distances| journal =[[Physical Review D]]| volume = 44| issue = 6| pages = 1731–1739| year = 1991| last1 = Jacobson | first1 = Theodore | bibcode = 1991PhRvD..44.1731J))</ref><ref>((Cite journal | doi = 10.1103/PhysRevD.52.4559|pmid=10019680|arxiv=hep-th/9506121| title = Hawking radiation without trans-Planckian frequencies| journal =[[Physical Review D]]| volume = 52| issue = 8| pages = 4559–4568| year = 1995| last1 = Brout | first1 = Robert | last2 = Massar | first2 = Serge | last3 = Parentani | first3 = Renaud | last4 = Spindel | first4 = Philippe |bibcode=1995PhRvD..52.4559B|s2cid=26432764))</ref>

The trans-Planckian problem is nowadays mostly considered a mathematical artifact of horizon calculations. The same effect occurs for regular matter falling onto a [[white hole]] solution. Matter that falls on the white hole accumulates on it, but has no future region into which it can go. Tracing the future of this matter, it is compressed onto the final singular endpoint of the white hole evolution, into a trans-Planckian region. The reason for these types of divergences is that modes that end at the horizon from the point of view of outside coordinates are singular in frequency there. The only way to determine what happens classically is to extend in some other coordinates that cross the horizon.

There exist alternative physical pictures that give the Hawking radiation in which the trans-Planckian problem is addressed.((citation needed|date=August 2016)) The key point is that similar trans-Planckian problems occur when the modes occupied with Unruh radiation are traced back in time.<ref name="witt-blah">For an alternative derivation and more detailed discussion of Hawking radiation as a form of Unruh radiation, see: ((cite book|last=de Witt |first=Bryce |date=1980 |contribution=Quantum gravity: the new synthesis |page=[https://archive.org/details/generalrelativit00isra/page/n711 696] |title=General Relativity: An Einstein Centenary Survey |publisher=Cambridge University Press |url=https://archive.org/details/generalrelativit00isra |url-access=limited |editor1-first=Stephen W. |editor1-last=Hawking |editor2-first=Werner |editor2-last=Israel |isbn=0-521-29928-4))</ref> In the Unruh effect, the magnitude of the temperature can be calculated from ordinary [[Hermann Minkowski|Minkowski]] field theory, and is not controversial.

===Large extra dimensions===
The formulas from the previous section are applicable only if the laws of gravity are approximately valid all the way down to the Planck scale. In particular, for black holes with masses below the Planck mass (~((val|e=-8|u=kg))), they result in impossible lifetimes below the Planck time (~((val|e=-43|u=s))). This is normally seen as an indication that the Planck mass is the lower limit on the mass of a black hole.

In a model with [[large extra dimensions]] (10 or 11), the values of Planck constants can be radically different, and the formulas for Hawking radiation have to be modified as well. In particular, the lifetime of a micro black hole with a radius below the scale of the extra dimensions is given by equation 9 in Cheung (2002)<ref>((cite journal|last1=Cheung|first1=Kingman|title=Black Hole Production and Large Extra Dimensions|arxiv=hep-ph/0110163|doi=10.1103/PhysRevLett.88.221602|pmid=12059412|journal=[[Physical Review Letters]]|volume=88|issue=22|page=221602|date=2002|bibcode=2002PhRvL..88v1602C|s2cid=14228817))</ref> and equations 25 and 26 in Carr (2005).<ref>((Cite book |last1=Carr |first1=Bernard J. |chapter=Primordial Black Holes – Recent Developments|arxiv=astro-ph/0504034|date=2005|title=Proceedings of the 22nd Texas Symposium on Relativistic Astrophysics at Stanford, Stanford California, December 13–17, 2004 |editor1=Pisin Chen |editor2=Elliott Bloom |editor3=Greg Madejski |editor4=Vahe Patrosian |journal=22nd Texas Symposium on Relativistic Astrophysics|volume=041213|pages=89–100|bibcode=2005tsra.conf...89C))</ref>

: <math>\tau \sim \frac{1}{M_*} \left( \frac{M_\text{BH)){M_*} \right)^\frac{n+3}{n+1}, </math>

where ((math|''M''<sub>∗</sub>)) is the low-energy scale, which could be as low as a few TeV, and ((mvar|n)) is the number of large extra dimensions. This formula is now consistent with black holes as light as a few TeV, with lifetimes on the order of the "new Planck time" ~((val|e=-26|u=s)).

===In loop quantum gravity===
A detailed study of the quantum geometry of a black hole [[event horizon]] has been made using [[loop quantum gravity]].<ref name="url[2001.08833] Black Hole evaporation: A Perspective from Loop Quantum Gravity">((cite journal |title=Black Hole Evaporation: A Perspective from Loop Quantum Gravity |year=2020 |doi=10.3390/universe6020021 |arxiv=2001.08833 |last1=Ashtekar |first1=Abhay |journal=Universe |volume=6 |issue=2 |page=21 |bibcode=2020Univ....6...21A |doi-access=free ))</ref><ref>((Cite journal | doi = 10.1103/PhysRevLett.80.904 | last1 = Ashtekar  | first1 = Abhay | last2 = Baez | first2 = John Carlos | last3 = Corichi | first3 = Alejandro | last4 = Krasnov | first4 = Kirill | title = Quantum Geometry and Black Hole Entropy | bibcode=1998PhRvL..80..904A | volume=80 | issue = 5  | journal=[[Physical Review Letters]]| pages=904–907|arxiv = gr-qc/9710007 | year = 1998  | s2cid = 18980849 ))</ref> Loop-quantization does not reproduce the result for [[black hole entropy]] originally discovered by [[Jacob Bekenstein|Bekenstein]] and [[Stephen Hawking|Hawking]], unless the value of [[Immirzi parameter|a free parameter]] is set to cancel out various constants such that the Bekenstein–Hawking entropy formula is reproduced. However, [[quantum gravity|quantum gravitational]] corrections to the entropy and radiation of black holes have been computed based on the theory.

Based on the fluctuations of the horizon area, a quantum black hole exhibits deviations from the Hawking radiation spectrum that would be observable were [[X-ray]]s from Hawking radiation of evaporating [[primordial black holes]] to be observed.<ref>((Cite journal | doi = 10.1016/j.nuclphysb.2007.01.009 | last1 = Ansari  | first1 = Mohammad H.  | title = Spectroscopy of a canonically quantized horizon | bibcode=2007NuPhB.783..179A | volume=783 | issue = 3  | journal=[[Nuclear Physics B]]| pages=179–212|arxiv = hep-th/0607081 | year = 2007  | s2cid = 9966483 ))</ref> The quantum effects are centered at a set of discrete and unblended frequencies highly pronounced on top of the Hawking spectrum.<ref>((Cite journal | doi = 10.1016/j.nuclphysb.2007.11.038  | last1 = Ansari  | first1 = Mohammad H.  | title = Generic degeneracy and entropy in loop quantum gravity | bibcode=2008NuPhB.795..635A | volume=795 | issue = 3  | journal=[[Nuclear Physics B]]| pages=635–644|arxiv = gr-qc/0603121 | year = 2008  | s2cid = 119039723 ))</ref>

==Experimental observation==

===Astronomical search===

In June 2008, [[NASA]] launched the [[Fermi Gamma-ray Space Telescope|Fermi space telescope]], which is searching for the terminal gamma-ray flashes expected from evaporating [[primordial black hole]]s.  As of Jan 1st, 2023, none have been detected.<ref name="Fermi2018">((cite arXiv | last=Fermi-LAT collaboration | eprint=1802.00100 | title = Search for Gamma-Ray Emission from Local Primordial Black Holes with the Fermi Large Area Telescope | class=astro-ph | date=January 31, 2018 ))</ref>

===Heavy-ion collider physics===

If speculative [[large extra dimension]] theories are correct, then [[CERN]]'s [[Large Hadron Collider]] may be able to create micro black holes and observe their evaporation. No such micro black hole has been observed at CERN.<ref>((Cite journal | doi = 10.1103/PhysRevD.65.056010|arxiv=hep-ph/0106219| title = High energy colliders as black hole factories: The end of short distance physics| journal =[[Physical Review D]]| volume = 65| issue = 5|page=056010| year = 2002|author1-link=Steven Giddings| last1 = Giddings | first1 = Steven B. | last2 = Thomas | first2 = Scott |bibcode=2002PhRvD..65e6010G|s2cid=1203487))</ref><ref>((Cite journal | doi = 10.1103/PhysRevLett.87.161602| pmid = 11690198| title = Black Holes at the Large Hadron Collider| journal =[[Physical Review Letters]]| volume = 87| issue = 16| page = 161602| year = 2001| last1 = Dimopoulos | first1 = Savas | last2 = Landsberg | first2 = Greg | bibcode = 2001PhRvL..87p1602D|arxiv = hep-ph/0106295 | s2cid = 119375071))</ref><ref name="courier">((cite web |url=https://cerncourier.com/a/the-case-for-mini-black-holes/ |title=The Case for Mini Black Holes |work=[[CERN Courier]] |date= November 2004 |first1=Aurélien |last1=Barrau |first2=Julien |last2=Grain ))</ref><ref>((cite news| url=http://www.timesonline.co.uk/tol/news/uk/science/article4715761.ece | work=[[The Times]] | location=London | title=Stephen Hawkings 50 bet on the world the universe and the God particle | first=Mark | last=Henderson | date=September 9, 2008 | access-date=May 4, 2010))</ref>

===Experimental===
Under experimentally achievable conditions for gravitational systems, this effect is too small to be observed directly. It was predicted that Hawking radiation could be studied by analogy using [[sonic black hole]]s, in which [[phonon|sound perturbations]] are analogous to light in a gravitational black hole and the flow of an approximately [[perfect fluid]] is analogous to gravity (see ''[[Analog models of gravity]]'').<ref>((cite journal|last1=Barceló|first1=Carlos|last2=Liberati|first2=Stefano|last3=Visser|first3=Matt|date=2003|title=Towards the observation of Hawking radiation in Bose–Einstein condensates|journal=[[International Journal of Modern Physics A]]|volume=18|issue=21|pages=3735–3745|arxiv=gr-qc/0110036|bibcode=2003IJMPA..18.3735B|doi=10.1142/s0217751x0301615x|s2cid=1321910))</ref> Observations of Hawking radiation were reported, in [[sonic black hole]]s employing [[Bose–Einstein condensate]]s.<ref>((cite journal|last=Steinhauer|first=Jeff|date=2016|title=Observation of quantum Hawking radiation and its entanglement in an analogue black hole|url=http://www.nature.com/articles/nphys3863.epdf|journal=[[Nature Physics]]|volume=12|issue=10|pages=959–965|arxiv=1510.00621|bibcode=2016NatPh..12..959S|doi=10.1038/nphys3863|s2cid=119197166))</ref><ref>((Cite journal|last1=Muñoz de Nova|first1=Juan Ramón|last2=Golubkov|first2=Katrine|last3=Kolobov|first3=Victor I.|last4=Steinhauer|first4=Jeff|date=May 2019|title=Observation of thermal Hawking radiation and its temperature in an analogue black hole|url=https://www.nature.com/articles/s41586-019-1241-0|journal=Nature|language=en|volume=569|issue=7758|pages=688–691|doi=10.1038/s41586-019-1241-0|pmid=31142857|arxiv=1809.00913|bibcode=2019Natur.569..688M|s2cid=119327617|issn=1476-4687))</ref><ref>((Cite journal|last1=Kolobov|first1=Victor I.|last2=Golubkov|first2=Katrine|last3=Muñoz de Nova|first3=Juan Ramón|last4=Steinhauer|first4=Jeff|date=March 2021|title=Observation of stationary spontaneous Hawking radiation and the time evolution of an analogue black hole|url=https://www.nature.com/articles/s41567-020-01076-0|journal=Nature Physics|language=en|volume=17|issue=3|pages=362–367|doi=10.1038/s41567-020-01076-0|arxiv=1910.09363|bibcode=2021NatPh..17..362K|s2cid=230508375|issn=1745-2481))</ref>

In September 2010 an experimental set-up created a laboratory "white hole event horizon" that the experimenters claimed was shown to radiate an optical analog to Hawking radiation.<ref>((cite journal |url=http://www.technologyreview.com/blog/arxiv/25805/ |title=First Observation of Hawking Radiation |journal=MIT Technology Review |date=September 27, 2010 |author=Emerging Technology from the arXiv |access-date=September 27, 2010 |archive-date=March 1, 2012 |archive-url=https://web.archive.org/web/20120301205626/http://www.technologyreview.com/blog/arxiv/25805/ |url-status=dead ))</ref> However, the results remain unverified and debatable,<ref name="Milanoguys">((cite journal|title=Hawking radiation from ultrashort laser pulse filaments |first1=Francesco D. |last1=Belgiorno |first2=Sergio Luigi |last2=Cacciatori |first3=Matteo |last3=Clerici |first4=Vittorio |last4=Gorini |first5=Giovanni |last5=Ortenzi |first6=Luca |last6=Rizzi |first7=Eleonora |last7=Rubino |first8=Vera Giulia |last8=Sala |first9=Daniele |last9=Faccio |arxiv=1009.4634 |doi=10.1103/PhysRevLett.105.203901 |pmid=21231233 |date=2010 |journal=[[Physical Review Letters]]|volume=105 |issue=20 |page=203901 |bibcode=2010PhRvL.105t3901B|s2cid=2245320 ))</ref><ref>((cite news|title=Ultrafast Laser Pulse Makes Desktop Black Hole Glow|newspaper=[[Wired (magazine)|Wired]]|date=September 29, 2010|first=Lisa|last=Grossman|url=https://www.wired.com/wiredscience/2010/09/hawking-radiation-in-the-lab/|access-date=April 30, 2012))</ref> and its status as a genuine confirmation remains in doubt.<ref>((cite news|last=Matson |first=John|title=Artificial event horizon emits laboratory analog to theoretical black hole radiation|journal=[[Scientific American]]|date=October 1, 2010|url=http://www.scientificamerican.com/article.cfm?id=hawking-radiation))</ref>

==See also==
((div col|colwidth=30)) 
* [[Black hole information paradox]]
* [[Black hole thermodynamics]]
* [[Black hole starship]]
* [[Blandford–Znajek process]] and [[Penrose process]], other extractions of black-hole energy
* [[Gibbons–Hawking effect]]
* [[Thorne–Hawking–Preskill bet]]
* [[Unruh effect]]
((div col end))

==References==
((Reflist))

==Further reading==
((columns list|colwidth=30em|
* ((cite journal |last=Hawking |first=Stephen W. |author-link= Stephen Hawking|date=1974 |title=Black hole explosions? |journal=[[Nature (journal)|Nature]]|volume=248 |issue=5443 |pages=30–31 |doi=10.1038/248030a0 |bibcode = 1974Natur.248...30H |s2cid=4290107 )) → Hawking's first article on the topic
* ((cite journal |last=Page |first=Don N. |author-link= Don Page (physicist)|date=1976 |title=Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole |journal=[[Physical Review D]]|volume=13 |issue=2 |pages=198–206 |doi=10.1103/PhysRevD.13.198 |bibcode = 1976PhRvD..13..198P )) → first detailed studies of the evaporation mechanism
* ((cite journal |last1=Carr |first1=Bernard J. |last2=Hawking |first2=Stephen W. |author2-link=Stephen Hawking |date=1974 |title=Black holes in the early universe |journal=[[Monthly Notices of the Royal Astronomical Society ]]|volume=168 |issue=2 |pages=399–415 |bibcode=1974MNRAS.168..399C |doi=10.1093/mnras/168.2.399|arxiv=1209.2243 )) → links between primordial black holes and the early universe
* ((cite journal |last=Barrau |first=Aurélien |display-authors=etal |date=2002 |title=Antiprotons from primordial black holes |journal=[[Astronomy & Astrophysics]]|volume=388 |issue= 2|pages=676–687 |doi=10.1051/0004-6361:20020313 |arxiv = astro-ph/0112486 |bibcode = 2002A&A...388..676B |s2cid=17033284 ))
* ((cite journal |last=Barrau |first=Aurélien |display-authors=etal |date=2003 |title=Antideuterons as a probe of primordial black holes |journal=[[Astronomy & Astrophysics]]|volume=398 |issue= 2|pages=403–410 |doi=10.1051/0004-6361:20021588 |arxiv = astro-ph/0207395 |bibcode = 2003A&A...398..403B |s2cid=5727582 ))
* ((cite journal |last1=Barrau |first1=Aurélien |last2=Féron |first2=Chloé |last3=Grain |first3=Julien |date=2005 |title=Astrophysical Production of Microscopic Black Holes in a Low-Planck-Scale World |journal=[[The Astrophysical Journal]]|volume=630 |issue= 2|pages=1015–1019 |doi=10.1086/432033 |arxiv = astro-ph/0505436 |bibcode = 2005ApJ...630.1015B |s2cid=6411086 )) → experimental searches for primordial black holes thanks to the emitted antimatter
* ((cite arXiv |last1=Barrau |first1=Aurélien |last2=Boudoul |first2=Gaëlle |title=Some aspects of primordial black hole physics |eprint=astro-ph/0212225 |year=2002 )) → cosmology with primordial black holes
* ((cite journal |last1=Barrau |first1=Aurélien |last2=Grain |first2=Julien |last3=Alexeyev |first3=Stanislav O. |date=2004 |title=Gauss–Bonnet black holes at the LHC: beyond the dimensionality of space |journal=[[Physics Letters B]]|volume=584 |issue=1–2 |pages=114–122 |doi=10.1016/j.physletb.2004.01.019 |arxiv = hep-ph/0311238 |bibcode = 2004PhLB..584..114B |s2cid=14275281 )) → searches for new physics (quantum gravity) with primordial black holes
* ((cite journal |last=Kanti |first=Panagiota |date=2004 |title=Black Holes in Theories with Large Extra Dimensions: a Review |journal=[[International Journal of Modern Physics A]]|volume=19 |issue=29 |pages=4899–4951 |doi=10.1142/S0217751X04018324 |arxiv = hep-ph/0402168 |bibcode = 2004IJMPA..19.4899K |s2cid=11863375 )) → evaporating black holes and extra-dimensions
* ((cite journal|first1=Daisuke |last1=Ida |first2=Kin'ya |last2=Oda |first3=Seong-chan |last3=Park |arxiv=hep-th/0212108 |journal=[[Physical Review D]]|volume=67 |issue=6 |date=2003 |page=064025 |title=Rotating black holes at future colliders: Greybody factors for brane fields |doi=10.1103/PhysRevD.67.064025|bibcode=2003PhRvD..67f4025I ))
* ((cite journal|first1=Daisuke |last1=Ida |first2=Kin'ya |last2=Oda |first3=Seong-chan |last3=Park |arxiv=hep-th/0503052 |journal=[[Physical Review D]]|volume=71 |issue=12 |date=2005 |page=124039 |title=Rotating black holes at future colliders. II. Anisotropic scalar field emission |doi=10.1103/PhysRevD.71.124039|bibcode=2005PhRvD..71l4039I |s2cid=28276606 ))
* ((cite journal|first1=Daisuke |last1=Ida |first2=Kin'ya |last2=Oda |first3=Seong-chan |last3=Park |arxiv=hep-th/0602188 |journal=[[Physical Review D]]|volume=73 |issue=12 |date=2006 |page=124022 |title=Rotating Black Holes at Future Colliders. III. Determination of Black Hole Evolution |doi=10.1103/PhysRevD.73.124022|bibcode=2006PhRvD..73l4022I |s2cid=6702415 )) → determination of black hole's life and extra dimensions
* ((cite journal|first1=Nistor |last1=Nicolaevici |journal=[[Journal of Physics A ]]|volume=36 |issue=27 |date=2003 |pages=7667–7677 |doi=10.1088/0305-4470/36/27/317 |title=Blackbody spectrum from accelerated mirrors with asymptotically inertial trajectories|bibcode=2003JPhA...36.7667N |s2cid=121117052 )) → consistent derivation of the Hawking radiation in the Fulling–Davies mirror model.
* ((cite journal|author-link=Lee Smolin|first=Lee |last=Smolin |archive-url=https://web.archive.org/web/20080910170107/http://www.physicstoday.org/vol-59/iss-11/pdf/vol59no11p44_48.pdf |url=http://www.physicstoday.org/vol-59/iss-11/pdf/vol59no11p44_48.pdf |archive-date=September 10, 2008 |title=Quantum gravity faces reality |date=November 2006 |journal=Physics Today|volume=59 |issue=11 |pages=44–48 |bibcode=2006PhT....59k..44S |doi=10.1063/1.2435646 )) consists of the recent developments and predictions of [[loop quantum gravity]] about gravity in small scales including the deviation from Hawking radiation effect by [[Mohammad H. Ansari|Ansari]].
* ((cite journal|author-link=Mohammad H. Ansari|last=Ansari |first=Mohammad H. |arxiv=hep-th/0607081 |title=Spectroscopy of a canonically quantized horizon |journal=[[Nuclear Physics B]]|volume=783 |issue=3 |pages=179–212 |date=2007 |doi=10.1016/j.nuclphysb.2007.01.009 |bibcode=2007NuPhB.783..179A|s2cid=9966483 )) → studies the deviation of a loop quantized black hole from Hawking radiation. A novel observable quantum effect of black hole quantization is introduced.
* ((cite book|first1=Stuart L. |last1=Shapiro |first2=Saul A. |last2=Teukolsky |date=1983 |title=Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects |url=https://archive.org/details/blackholeswhited00shap_896 |url-access=limited |page=[https://archive.org/details/blackholeswhited00shap_896/page/n386 366] |publisher=Wiley-Interscience |isbn=978-0-471-87316-7)) → Hawking radiation evaporation formula derivation.
* ((Cite journal| last1 = Leonhardt | first1 = Ulf | last2= Maia |first2=Clovis |last3= Schuetzhold |first3=Ralf | date = 2010 | title = Focus on Classical and Quantum Analogs for Gravitational Phenomena and Related Effects | journal =[[New Journal of Physics ]]| volume = 14 | issue = 10| pages =105032 | doi = 10.1088/1367-2630/14/10/105032| bibcode = 2012NJPh...14j5032L | doi-access = free | hdl = 10023/4760 | hdl-access = free ))
))

==External links==
* [https://web.archive.org/web/20081014010322/http://xaonon.dyndns.org/hawking/ Hawking radiation calculator tool]
* [https://cerncourier.com/the-case-for-mini-black-holes/ The case for mini black holes] A. Barrau & J. Grain explain how the Hawking radiation could be detected at colliders

((quantum gravity))
((Stephen Hawking))
((Authority control))
((Portal bar|Astronomy|Physics))

((DEFAULTSORT:Hawking Radiation))
[[Category:Black holes]]
[[Category:Quantum field theory]]
[[Category:Stephen Hawking|Radiation]]
[[Category:Astronomical hypotheses]]
[[Category:Hypothetical processes]]
[[Category:1974 introductions]]

Pages transcluded onto the current version of this page (help):

Hawking radiation (edit)
Template:Ambox (view source) (template editor protected)
Template:Authority control (view source) (template editor protected)
Template:Category-inline (view source) (template editor protected)
Template:Category handler (view source) (protected)
Template:Citation needed (view source) (protected)
Template:Cite arXiv (view source) (template editor protected)
Template:Cite book (view source) (protected)
Template:Cite journal (view source) (protected)
Template:Cite news (view source) (protected)
Template:Cite web (view source) (protected)
Template:Clarify (view source) (template editor protected)
Template:Columns-list (view source) (template editor protected)
Template:Columns list (edit)
Template:DMCA (view source) (template editor protected)
Template:Dated maintenance category (view source) (template editor protected)
Template:Dated maintenance category (articles) (view source) (template editor protected)
Template:Dead link (view source) (template editor protected)
Template:Delink (view source) (protected)
Template:Div col (view source) (template editor protected)
Template:Div col/styles.css (view source) (template editor protected)
Template:Div col end (view source) (template editor protected)
Template:FULLROOTPAGENAME (view source) (template editor protected)
Template:Fix (view source) (protected)
Template:Fix-span (view source) (template editor protected)
Template:Fix/category (view source) (protected)
Template:General relativity sidebar (edit)
Template:Hlist (view source) (protected)
Template:Hlist/styles.css (view source) (protected)
Template:Icon (view source) (template editor protected)
Template:JULIANDAY (view source) (template editor protected)
Template:MONTHNAME (view source) (template editor protected)
Template:MONTHNUMBER (view source) (template editor protected)
Template:Main other (view source) (protected)
Template:Math (view source) (template editor protected)
Template:More citations needed (view source) (template editor protected)
Template:More citations needed section (view source) (template editor protected)
Template:Mvar (view source) (template editor protected)
Template:Navbox (view source) (template editor protected)
Template:Nowrap (view source) (protected)
Template:Ns has subpages (view source) (protected)
Template:Pagetype (view source) (protected)
Template:Plainlist/styles.css (view source) (protected)
Template:Portal-inline (view source) (template editor protected)
Template:Portal bar (view source) (template editor protected)
Template:Quantum gravity (edit)
Template:R/superscript (view source) (template editor protected)
Template:R/where (view source) (template editor protected)
Template:Reflist (view source) (protected)
Template:Reflist/styles.css (view source) (protected)
Template:Rp (view source) (template editor protected)
Template:SDcat (view source) (protected)
Template:Sfrac (view source) (extended confirmed protected)
Template:Sfrac/styles.css (view source) (extended confirmed protected)
Template:Short description (view source) (protected)
Template:Short description/lowercasecheck (view source) (protected)
Template:Sidebar (view source) (template editor protected)
Template:Sidebar with collapsible lists (view source) (template editor protected)
Template:Solar mass (view source) (template editor protected)
Template:Sp (view source) (template editor protected)
Template:Stephen Hawking (edit)
Template:Subinfobox bodystyle (view source) (template editor protected)
Template:Subsidebar bodystyle (view source) (template editor protected)
Template:Update after (view source) (template editor protected)
Template:Update inline span (view source) (template editor protected)
Template:Update span (view source) (template editor protected)
Template:Val (view source) (template editor protected)
Template:Verify source (view source) (template editor protected)
Module:Arguments (view source) (protected)
Module:Authority control (view source) (template editor protected)
Module:Authority control/auxiliary (view source) (template editor protected)
Module:Authority control/config (view source) (template editor protected)
Module:Category handler (view source) (protected)
Module:Category handler/blacklist (view source) (protected)
Module:Category handler/config (view source) (protected)
Module:Category handler/data (view source) (protected)
Module:Category handler/shared (view source) (protected)
Module:Check for unknown parameters (view source) (protected)
Module:Citation/CS1 (view source) (protected)
Module:Citation/CS1/COinS (view source) (protected)
Module:Citation/CS1/Configuration (view source) (protected)
Module:Citation/CS1/Date validation (view source) (protected)
Module:Citation/CS1/Identifiers (view source) (protected)
Module:Citation/CS1/Utilities (view source) (protected)
Module:Citation/CS1/Whitelist (view source) (protected)
Module:Citation/CS1/styles.css (view source) (protected)
Module:Convert (view source) (template editor protected)
Module:Convert/data (view source) (template editor protected)
Module:Convert/text (view source) (template editor protected)
Module:DecodeEncode (view source) (template editor protected)
Module:Delink (view source) (protected)
Module:Disambiguation/templates (view source) (protected)
Module:EditAtWikidata (view source) (protected)
Module:Gapnum (view source) (extended confirmed protected)
Module:GetParameters (view source) (template editor protected)
Module:Icon (view source) (template editor protected)
Module:Icon/data (view source) (template editor protected)
Module:List (view source) (protected)
Module:Message box (view source) (protected)
Module:Message box/ambox.css (view source) (protected)
Module:Message box/configuration (view source) (protected)
Module:Namespace detect/config (view source) (protected)
Module:Namespace detect/data (view source) (protected)
Module:Navbar (view source) (protected)
Module:Navbar/configuration (view source) (protected)
Module:Navbar/styles.css (view source) (protected)
Module:Navbox (view source) (template editor protected)
Module:Navbox/configuration (view source) (template editor protected)
Module:Navbox/styles.css (view source) (template editor protected)
Module:Ns has subpages (view source) (protected)
Module:Pagetype (view source) (protected)
Module:Pagetype/config (view source) (protected)
Module:Pagetype/disambiguation (view source) (protected)
Module:Pagetype/setindex (view source) (protected)
Module:Pagetype/softredirect (view source) (protected)
Module:Plain text (view source) (template editor protected)
Module:Portal (view source) (template editor protected)
Module:Portal-inline (view source) (template editor protected)
Module:Portal/images/a (view source) (template editor protected)
Module:Portal/images/p (view source) (template editor protected)
Module:Portal bar (view source) (template editor protected)
Module:Portal bar/styles.css (view source) (template editor protected)
Module:SDcat (view source) (protected)
Module:Sidebar (view source) (template editor protected)
Module:Sidebar/configuration (view source) (template editor protected)
Module:Sidebar/styles.css (view source) (template editor protected)
Module:String (view source) (protected)
Module:String2 (view source) (template editor protected)
Module:TableTools (view source) (protected)
Module:Template wrapper (view source) (template editor protected)
Module:Unsubst (view source) (protected)
Module:Val (view source) (template editor protected)
Module:Val/units (view source) (template editor protected)
Module:Wikitext Parsing (view source) (protected)
Module:Yesno (view source) (protected)

Return to Hawking radiation.

Retrieved from "https://en.wikipedia.org/wiki/Hawking_radiation"