Hawking radiation
Hawking radiation is blackbody radiation that is predicted to be released by black holes, due to quantum effects near the black hole event horizon. It is named after the theoretical physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974.[1]
Part of a series of articles about  
General relativity  

Fundamental concepts 

Phenomena 



Hawking radiation reduces the mass and rotational energy of black holes and is therefore also known as black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish. Micro black holes are predicted to be larger emitters of radiation than more massive black holes and should thus shrink and dissipate faster.
In June 2008, NASA launched the Fermi space telescope, which is searching for the terminal gammaray flashes expected from evaporating primordial black holes. In the event that speculative large extra dimension theories are correct, CERN's Large Hadron Collider may be able to create micro black holes and observe their evaporation. No such micro black hole has ever been observed at CERN.[2][3][4][5]
In September 2010, a signal that is closely related to black hole Hawking radiation (see analog gravity) was claimed to have been observed in a laboratory experiment involving optical light pulses. However, the results remain unverified and debatable.[6][7] Other projects have been launched to look for this radiation within the framework of analog gravity.
Overview
Black holes are sites of immense gravitational attraction. Classically, the gravitation generated by the gravitational singularity inside a black hole is so powerful that nothing, not even electromagnetic radiation, can escape from the black hole. It is yet unknown how gravity can be incorporated into quantum mechanics. Nevertheless, far from the black hole, the gravitational effects can be weak enough for calculations to be reliably performed in the framework of quantum field theory in curved spacetime. Hawking showed that quantum effects allow black holes to emit exact blackbody radiation. The electromagnetic radiation is produced as if emitted by a black body with a temperature inversely proportional to the mass of the black hole.
Physical insight into the process may be gained by imagining that particle–antiparticle radiation is emitted from just beyond the event horizon. This radiation does not come directly from the black hole itself, but rather is a result of virtual particles being "boosted" by the black hole's gravitation into becoming real particles. As the particle–antiparticle pair was produced by the black hole's gravitational energy, the escape of one of the particles lowers the mass of the black hole.[8]
An alternative view of the process is that vacuum fluctuations cause a particle–antiparticle pair to appear close to the event horizon of a black hole. One of the pair falls into the black hole while the other escapes. In order to preserve total energy, the particle that fell into the black hole must have had a negative energy (with respect to an observer far away from the black hole). This causes the black hole to lose mass, and, to an outside observer, it would appear that the black hole has just emitted a particle. In another model, the process is a quantum tunnelling effect, whereby particle–antiparticle pairs will form from the vacuum, and one will tunnel outside the event horizon.
An important difference between the black hole radiation as computed by Hawking and thermal radiation emitted from a black body is that the latter is statistical in nature, and only its average satisfies what is known as Planck's law of blackbody radiation, while the former fits the data better. Thus thermal radiation contains information about the body that emitted it, while Hawking radiation seems to contain no such information, and depends only on the mass, angular momentum, and charge of the black hole (the nohair theorem). This leads to the black hole information paradox.
However, according to the conjectured gaugegravity 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 nonzero 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. If this is correct, then Hawking's original calculation should be corrected, though it is not known how (see below).
A black hole of one solar mass (M_{☉}) has a temperature of only 60 nanokelvins (60 billionths of a kelvin); in fact, such a black hole would absorb far more cosmic microwave background radiation than it emits. A black hole of 4.5×10^{22} kg (about the mass of the Moon, or about 133 μm across) would be in equilibrium at 2.7 K, absorbing as much radiation as it emits. Yet smaller primordial black holes would emit more than they absorb and thereby lose mass.
Discovery
Hawking's discovery followed a visit to Moscow in 1973 where the Soviet scientists Yakov Zel'dovich and Alexei Starobinsky convinced him that rotating black holes ought to create and emit particles. When Hawking did the calculation, he found to his surprise that even nonrotating black holes produce radiation.[9]
TransPlanckian problem
The transPlanckian 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 finite frequency, if traced back to the horizon, must have had an infinite frequency, and therefore a transPlanckian 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 shifts the modes.
An outgoing Hawkingradiated photon, 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 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.[10][11][12][13]
The transPlanckian 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 transPlanckian 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 transPlanckian problem is addressed. The key point is that similar transPlanckian problems occur when the modes occupied with Unruh radiation are traced back in time.[14] In the Unruh effect, the magnitude of the temperature can be calculated from ordinary Minkowski field theory, and is not controversial.
Emission process
Hawking radiation is required by 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 freefall 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.[14]
A Schwarzschild black hole has a metric:
 .
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
 .
The local metric to lowest order is
 ,
which is Rindler in terms of τ = t/4M. The metric describes a frame that is accelerating to keep from falling into the black hole. The local acceleration, α = ^{1}⁄_{ρ}, diverges as 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 nearhorizon observer must see the field excited at a local temperature
 ;
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 redshiftmatched to the near horizon temperature:
 .
The inverse temperature redshifted to r′ at infinity is
and r is the nearhorizon position, near 2M, so this is really:
 .
So a field theory defined on a black hole background is in a thermal state whose temperature at infinity is:
 .
This can be expressed in a cleaner way in terms of the surface gravity of the black hole; this is the parameter that determines the acceleration of a nearhorizon observer. In natural units (G = c = ħ = k_{B} = 1), the temperature is
 ,
where κ is the surface gravity of the horizon. So a black hole can only be in equilibrium with a gas of radiation at a finite temperature. Since radiation incident on the black hole is absorbed, the black hole must emit an equal amount to maintain detailed balance. The black hole acts as a perfect blackbody radiating at this temperature.
In SI units, the radiation from a Schwarzschild black hole is blackbody radiation with temperature
 ,
where ħ is the reduced Planck constant, c is the speed of light, k_{B} is the Boltzmann constant, G is the gravitational constant, M_{☉} is the solar mass, and M is the mass of the black hole.
From the black hole temperature, it is straightforward to calculate the black hole entropy. The change in entropy when a quantity of heat dQ is added is:
 .
The heat energy that enters serves to increase the total mass, so:
 .
The radius of a black hole is twice its mass in natural units, so the entropy of a black hole is proportional to its surface area:
 .
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 somehow encoded onto a bounding surface.
In 2019, Biancalana, Robson and Villari from HeriotWatt University in Edinburgh (UK), showed that Hawking's radiation temperature is a purely topological quantity that can be calculated very simply by computing the Euler characteristics of the black hole spacetime.[15]
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 Einstein's equation E = mc^{2}).
1976 Page numerical analysis
In 1976 Don Page calculated the power produced, and the time to evaporation, for a nonrotating, noncharged Schwarzschild black hole of mass M.[16] 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, spindependent manner as frequency decreases, especially when the wavelength becomes comparable to the size of the event horizon. Note that writing in 1976, Page erroneously postulates 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 3 flavors of neutrinos with nonzero masses.
For a mass much larger than 10^{17} grams, Page deduces that electron emission can be ignored, and that black holes of mass M in grams evaporate via massless electron and muon neutrinos, photons, and gravitons in a time τ of
For a mass much smaller than 10^{17} g, but much larger than 5×10^{14} g, the emission of ultrarelativistic electrons and positrons will accelerate the evaporation, giving a lifetime of
If black holes evaporate under Hawking radiation, a solar mass black hole will evaporate over 10^{64} years.[17] A supermassive black hole with a mass of 10^{11} (100 billion) M_{☉} will evaporate in around 2×10^{100} years.[18] Some monster black holes in the universe are predicted to continue to grow up to perhaps 10^{14} M_{☉} during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 10^{106} years.[17]
Large extra dimensions
The formulae 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 (~10^{−8} kg), they result in impossible lifetimes below the Planck time (~10^{−43} 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 formulae 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)[19] and equations 25 and 26 in Carr (2005).[20]
where M_{∗} is the low energy scale, which could be as low as a few TeV, and 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" ~10^{−26} 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.[21] Loopquantization reproduces the result for black hole entropy originally discovered by Bekenstein and Hawking. Further, it led to the computation of quantum gravity corrections to the entropy and radiation of black holes.
Based on the fluctuations of the horizon area, a quantum black hole exhibits deviations from the Hawking spectrum that would be observable were Xrays from Hawking radiation of evaporating primordial black holes to be observed.[22] The quantum effects are centered at a set of discrete and unblended frequencies highly pronounced on top of Hawking radiation spectrum.[23]
Experimental observation
Under experimentally achievable conditions for gravitational systems this effect is too small to be observed directly. However, in September 2010 an experimental setup created a laboratory "white hole event horizon" that the experimenters claimed was shown to radiate an optical analog to Hawking radiation,[24] although its status as a genuine confirmation remains in doubt.[25] Some scientists predict that Hawking radiation could be studied by analogy using sonic black holes, in which sound perturbations are analogous to light in a gravitational black hole and the flow of an approximately perfect fluid is analogous to gravity.[26][27]
See also
 Analog models of gravity
 Black hole starship
 Gibbons–Hawking effect
 Blandford–Znajek process and Penrose process, other extractions of blackhole energy
 Thorne–Hawking–Preskill bet
 Unruh effect
References
 Rose, Charlie. "A conversation with Dr. Stephen Hawking & Lucy Hawking". charlierose.com. Archived from the original on March 29, 2013.
 Giddings, Steven B.; Thomas, Scott (2002). "High energy colliders as black hole factories: The end of short distance physics". Physical Review D. 65 (5): 056010. arXiv:hepph/0106219. Bibcode:2002PhRvD..65e6010G. doi:10.1103/PhysRevD.65.056010.
 Dimopoulos, Savas; Landsberg, Greg (2001). "Black Holes at the Large Hadron Collider". Physical Review Letters. 87 (16): 161602. arXiv:hepph/0106295. Bibcode:2001PhRvL..87p1602D. doi:10.1103/PhysRevLett.87.161602. PMID 11690198.
 Barrau, Aurélien; Grain, Julien (November 2004). "The Case for Mini Black Holes". CERN Courier.
 Henderson, Mark (September 9, 2008). "Stephen Hawkings 50 bet on the world the universe and the God particle". The Times. London. Retrieved May 4, 2010.
 Belgiorno, Francesco D.; Cacciatori, Sergio Luigi; Clerici, Matteo; Gorini, Vittorio; Ortenzi, Giovanni; Rizzi, Luca; Rubino, Eleonora; Sala, Vera Giulia; Faccio, Daniele (2010). "Hawking radiation from ultrashort laser pulse filaments". Physical Review Letters. 105 (20): 203901. arXiv:1009.4634. Bibcode:2010PhRvL.105t3901B. doi:10.1103/PhysRevLett.105.203901. PMID 21231233.
 Grossman, Lisa (September 29, 2010). "Ultrafast Laser Pulse Makes Desktop Black Hole Glow". Wired. Retrieved April 30, 2012.
 Carroll, Bradley; Ostlie, Dale (1996). An Introduction to Modern Astrophysics. Addison Wesley. p. 673. ISBN 0201547309.
 Hawking, Stephen (1988). A Brief History of Time. Bantam Books. ISBN 0553380168.
 Helfer, Adam D. (2003). "Do black holes radiate?". Reports on Progress in Physics. 66 (6): 943–1008. arXiv:grqc/0304042. Bibcode:2003RPPh...66..943H. doi:10.1088/00344885/66/6/202.
 't Hooft, Gerard (1985). "On the quantum structure of a black hole". Nuclear Physics B. 256: 727–745. Bibcode:1985NuPhB.256..727T. doi:10.1016/05503213(85)904183.
 Jacobson, Theodore (1991). "Blackhole evaporation and ultrashort distances". Physical Review D. 44 (6): 1731–1739. Bibcode:1991PhRvD..44.1731J. doi:10.1103/PhysRevD.44.1731. PMID 10014053.
 Brout, Robert; Massar, Serge; Parentani, Renaud; Spindel, Philippe (1995). "Hawking radiation without transPlanckian frequencies". Physical Review D. 52 (8): 4559–4568. arXiv:hepth/9506121. Bibcode:1995PhRvD..52.4559B. doi:10.1103/PhysRevD.52.4559.
 For an alternative derivation and more detailed discussion of Hawking radiation as a form of Unruh radiation see de Witt, Bryce (1980). "Quantum gravity: the new synthesis". In Hawking, Stephen W.; Israel, Werner (eds.). General Relativity: An Einstein Centenary Survey. p. 696. ISBN 0521299284.
 Robson, Charles W.; Di Mauro Villari, Leone; Biancalana, Fabio (2019). "Topological nature of the Hawking temperature of black holes". Physical Review D. 99 (4): 044042. arXiv:1810.09322. Bibcode:2019PhRvD..99d4042R. doi:10.1103/PhysRevD.99.044042. ISSN 24700010.
 Page, Don N. (1976). "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole". Physical Review D. 13 (2): 198–206. Bibcode:1976PhRvD..13..198P. doi:10.1103/PhysRevD.13.198.
 See page 596: table 1 and the "black hole decay" section and previous sentence on that page in Frautschi, Steven (1982). "Entropy in an Expanding Universe". Science. 217 (4560): 593–599. Bibcode:1982Sci...217..593F. doi:10.1126/science.217.4560.593. PMID 17817517.
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^{14}M_{☉} ... the timescale for black holes to radiate away all their energy ranges from to 10^{64} years for black holes of one solar mass ...
 Page, Don N. (1976). "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole". Physical Review D. 13 (2): 198–206. Bibcode:1976PhRvD..13..198P. doi:10.1103/PhysRevD.13.198. See in particular equation (27).
 Cheung, Kingman (2002). "Black Hole Production and Large Extra Dimensions". Physical Review Letters. 88 (22): 221602. arXiv:hepph/0110163. Bibcode:2002PhRvL..88v1602C. doi:10.1103/PhysRevLett.88.221602. PMID 12059412.
 Carr, Bernard J. (2005). "Primordial Black Holes – Recent Developments". In Pisin Chen; Elliott Bloom; Greg Madejski; Vahe Patrosian (eds.). Proceedings of the 22nd Texas Symposium on Relativistic Astrophysics at Stanford, Stanford California, December 1317, 2004. pp. 89–100. arXiv:astroph/0504034. Bibcode:2005tsra.conf...89C.
 Ashtekar, Abhay; Baez, John Carlos; Corichi, Alejandro; Krasnov, Kirill (1998). "Quantum Geometry and Black Hole Entropy". Physical Review Letters. 80 (5): 904–907. arXiv:grqc/9710007. Bibcode:1998PhRvL..80..904A. doi:10.1103/PhysRevLett.80.904.
 Ansari, Mohammad H. (2007). "Spectroscopy of a canonically quantized horizon". Nuclear Physics B. 783 (3): 179–212. arXiv:hepth/0607081. Bibcode:2007NuPhB.783..179A. doi:10.1016/j.nuclphysb.2007.01.009.
 Ansari, Mohammad H. (2008). "Generic degeneracy and entropy in loop quantum gravity". Nuclear Physics B. 795 (3): 635–644. arXiv:grqc/0603121. Bibcode:2008NuPhB.795..635A. doi:10.1016/j.nuclphysb.2007.11.038.
 Emerging Technology from the arXiv (September 27, 2010). "First Observation of Hawking Radiation". MIT Technology Review.
 Matson, John (October 1, 2010). "Artificial event horizon emits laboratory analog to theoretical black hole radiation". Scientific American.
 Barceló, Carlos; Liberati, Stefano; Visser, Matt (2003). "Towards the observation of Hawking radiation in Bose–Einstein condensates". International Journal of Modern Physics A. 18 (21): 3735–3745. arXiv:grqc/0110036. Bibcode:2003IJMPA..18.3735B. doi:10.1142/s0217751x0301615x.
 Steinhauer, Jeff (2016). "Observation of quantum Hawking radiation and its entanglement in an analogue black hole". Nature Physics. 12 (10): 959–965. arXiv:1510.00621. Bibcode:2016NatPh..12..959S. doi:10.1038/nphys3863.
Further reading
 Hawking, Stephen W. (1974). "Black hole explosions?". Nature. 248 (5443): 30–31. Bibcode:1974Natur.248...30H. doi:10.1038/248030a0. → Hawking's first article on the topic
 Page, Don N. (1976). "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole". Physical Review D. 13 (2): 198–206. Bibcode:1976PhRvD..13..198P. doi:10.1103/PhysRevD.13.198. → first detailed studies of the evaporation mechanism
 Carr, Bernard J.; Hawking, Stephen W. (1974). "Black holes in the early universe". Monthly Notices of the Royal Astronomical Society . 168 (2): 399–415. arXiv:1209.2243. Bibcode:1974MNRAS.168..399C. doi:10.1093/mnras/168.2.399. → links between primordial black holes and the early universe
 Barrau, Aurélien; et al. (2002). "Antiprotons from primordial black holes". Astronomy & Astrophysics. 388 (2): 676–687. arXiv:astroph/0112486. Bibcode:2002A&A...388..676B. doi:10.1051/00046361:20020313.
 Barrau, Aurélien; et al. (2003). "Antideuterons as a probe of primordial black holes". Astronomy & Astrophysics. 398 (2): 403–410. arXiv:astroph/0207395. Bibcode:2003A&A...398..403B. doi:10.1051/00046361:20021588.
 Barrau, Aurélien; Féron, Chloé; Grain, Julien (2005). "Astrophysical Production of Microscopic Black Holes in a Low–PlanckScale World". The Astrophysical Journal. 630 (2): 1015–1019. arXiv:astroph/0505436. Bibcode:2005ApJ...630.1015B. doi:10.1086/432033. → experimental searches for primordial black holes thanks to the emitted antimatter
 Barrau, Aurélien; Boudoul, Gaëlle (2002). "Some aspects of primordial black hole physics". arXiv:astroph/0212225. → cosmology with primordial black holes
 Barrau, Aurélien; Grain, Julien; Alexeyev, Stanislav O. (2004). "Gauss–Bonnet black holes at the LHC: beyond the dimensionality of space". Physics Letters B. 584 (1–2): 114–122. arXiv:hepph/0311238. Bibcode:2004PhLB..584..114B. doi:10.1016/j.physletb.2004.01.019. → searches for new physics (quantum gravity) with primordial black holes
 Kanti, Panagiota (2004). "Black Holes in Theories with Large Extra Dimensions: a Review". International Journal of Modern Physics A. 19 (29): 4899–4951. arXiv:hepph/0402168. Bibcode:2004IJMPA..19.4899K. doi:10.1142/S0217751X04018324. → evaporating black holes and extradimensions
 Ida, Daisuke; Oda, Kin'ya; Park, Seongchan (2003). "Rotating black holes at future colliders: Greybody factors for brane fields". Physical Review D. 67 (6): 064025. arXiv:hepth/0212108. Bibcode:2003PhRvD..67f4025I. doi:10.1103/PhysRevD.67.064025.
 Ida, Daisuke; Oda, Kin'ya; Park, Seongchan (2005). "Rotating black holes at future colliders. II. Anisotropic scalar field emission". Physical Review D. 71 (12): 124039. arXiv:hepth/0503052. Bibcode:2005PhRvD..71l4039I. doi:10.1103/PhysRevD.71.124039.
 Ida, Daisuke; Oda, Kin'ya; Park, Seongchan (2006). "Rotating Black Holes at Future Colliders. III. Determination of Black Hole Evolution". Physical Review D. 73 (12): 124022. arXiv:hepth/0602188. Bibcode:2006PhRvD..73l4022I. doi:10.1103/PhysRevD.73.124022. → determination of black hole's life and extra dimensions
 Nicolaevici, Nistor (2003). "Blackbody spectrum from accelerated mirrors with asymptotically inertial trajectories". Journal of Physics A . 36 (27): 7667–7677. Bibcode:2003JPhA...36.7667N. doi:10.1088/03054470/36/27/317. → consistent derivation of the Hawking radiation in the Fulling–Davies mirror model.
 Smolin, Lee (November 2006). "Quantum gravity faces reality" (PDF). Physics Today. 59 (11): 44–48. Bibcode:2006PhT....59k..44S. doi:10.1063/1.2435646. Archived from the original (PDF) on September 10, 2008. consists of the recent developments and predictions of loop quantum gravity about gravity in small scales including the deviation from Hawking radiation effect by Ansari.
 Ansari, Mohammad H. (2007). "Spectroscopy of a canonically quantized horizon". Nuclear Physics B. 783 (3): 179–212. arXiv:hepth/0607081. Bibcode:2007NuPhB.783..179A. doi:10.1016/j.nuclphysb.2007.01.009. → studies the deviation of a loop quantized black hole from Hawking radiation. A novel observable quantum effect of black hole quantization is introduced.
 Shapiro, Stuart L.; Teukolsky, Saul A. (1983). Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects. WileyInterscience. p. 366. ISBN 9780471873167. → Hawking radiation evaporation formula derivation.
 Leonhardt, Ulf; Maia, Clovis; Schuetzhold, Ralf (2010). "Focus on Classical and Quantum Analogs for Gravitational Phenomena and Related Effects". New Journal of Physics . 14 (10): 105032. Bibcode:2012NJPh...14j5032L. doi:10.1088/13672630/14/10/105032.
External links
 Hawking radiation calculator tool
 The case for mini black holes A. Barrau & J. Grain explain how the Hawking radiation could be detected at colliders
 Black Holes – Anybody out there?
 University of Colorado at Boulder
 Hawking radiation on arxiv.org
 Hawking radiation observed in laboratory?