Can an Evaporating Black Hole Become a Star Again

Thermal radiation emitted outside the outcome horizon of a blackness pigsty

Hawking radiation is thermal radiation that is theorized to exist released outside a black pigsty's event horizon because of relativistic breakthrough effects. It is named after the physicist Stephen Hawking, who developed a theoretical statement for its being in 1974.^[ane] Hawking radiation is a purely kinematic effect that is generic to Lorentzian geometries containing event horizons or local credible horizons.^{[2] [iii]}

Hawking radiation reduces the mass and rotational energy of black holes and is therefore besides theorized to crusade black pigsty evaporation. Considering of this, black holes that practice non proceeds mass through other means are expected to shrink and ultimately vanish. For all except the smallest black holes, this would happen extremely slowly. The radiations temperature is inversely proportional to the blackness hole'due south mass, then micro black holes are predicted to be larger emitters of radiation than larger black holes and should dissipate faster.^[4]

Overview [edit]

Blackness holes are astrophysical objects of involvement primarily because of their meaty size and immense gravitational attraction. They were beginning predicted past Einstein's 1915 theory of general relativity, before astrophysical evidence began to mount half a century afterward.

A black pigsty tin grade when enough matter and/or energy is compressed into a volume small plenty that the escape velocity is greater than the speed of light. Nothing can travel that fast, so nothing inside a distance, proportional to the mass of the blackness hole, tin escape beyond that distance. The region beyond which not even light tin can escape is the upshot horizon; an observer outside it cannot discover, get aware of, or be afflicted by events within the consequence horizon. The essence of a black pigsty is its event horizon, a theoretical demarcation between events and their causal relationships.^{[5] : 25–36}

Alternatively, using a set of infalling coordinates in general relativity, one tin can conceptualize the event horizon equally the region beyond which space is infalling faster than the speed of light. (Although nothing can travel through infinite faster than calorie-free, space itself tin infall at whatsoever speed.)^[6] In one case matter is inside the outcome horizon, all of the matter inside falls inexorably into a gravitational singularity, a place of space curvature and zero size, leaving backside a warped spacetime devoid of any matter. A classical black hole is pure empty spacetime, and the simplest (nonrotating and uncharged) is characterized just by its mass and event horizon.^{[five] : 37–43}

Our current understandings of quantum physics tin be used to investigate what may happen in the region around the effect horizon. In 1974, British physicist Stephen Hawking used breakthrough field theory in curved spacetime to show that in theory, the force of gravity at the effect horizon was potent enough to crusade thermal radiation to be emitted and energy to "leak" into the wider universe from a tiny distance around and outside the event horizon. In effect this energy acted every bit if the blackness pigsty itself was slowly evaporating (although it actually came from outside it).^[seven]

An of import difference between the black pigsty radiation every bit computed past 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'south police force of blackness-trunk radiations, while the former fits the information amend. Thus, thermal radiation contains data about the torso that emitted it, while Hawking radiation seems to contain no such information, and depends only on the mass, angular momentum, and accuse of the black hole (the no-hair theorem). This leads to the black hole information paradox.

Even so, according to the conjectured gauge-gravity duality (also known as the AdS/CFT correspondence), black holes in sure cases (and perhaps in general) are equivalent to solutions of quantum field theory at a non-zero temperature. This ways that no information loss is expected in black holes (since the theory permits no such loss) and the radiation emitted past a blackness 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 sixty nanokelvins (60 billionths of a kelvin); in fact, such a blackness hole would blot far more cosmic microwave background radiation than it emits. A black hole of 4.5×10²² 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 information technology emits.^{[ commendation needed ]}

Discovery [edit]

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, while Russian physicist Vladimir Gribov believed that even a non-rotating black hole should emit radiation. When Hawking did the calculation, he institute to his surprise that even non-rotating black holes produce radiation.^[8] In 1972, Jacob Bekenstein conjectured that the black holes should have an entropy,^[ix] where by the aforementioned year, he proposed no hair theorems. Bekenstein's discovery and results are commended by Stephen Hawking which also led him to think about radiations due to this formalism.

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 just a rotating black hole could emit radiation, while Gribov believed that fifty-fifty a non-rotating blackness hole emits radiation due to the laws of quantum mechanics.^{[10] [11]} This business relationship is confirmed by Gribov's obituary in the Physics-Uspekhi by Vitaly Ginzburg and others.^{[12] [13]}

Emission process [edit]

Hawking radiation is required past 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 go along from falling in. An accelerating observer sees a thermal bathroom of particles that pop out of the local dispatch horizon, plough around, and gratuitous-fall back in. The condition of local thermal equilibrium implies that the consistent extension of this local thermal bathroom has a finite temperature at infinity, which implies that some of these particles emitted past the horizon are not reabsorbed and become outgoing Hawking radiations.^{[14] [xv]}

A Schwarzschild black hole has a metric:

${\displaystyle \left(\mathrm {d} due south\correct)^{two}=-\left(1-{\tfrac {2M}{r}}\right)\,\left(\mathrm {d} t\right)^{2}+{\frac {ane}{\left(i-{\frac {2M}{r}}\right)}}\,\left(\mathrm {d} r\right)^{2}+r^{2}\,\left(\mathrm {d} \Omega \correct)^{2}\,}$ .

The black pigsty is the groundwork spacetime for a breakthrough field theory.

The field theory is defined by a local path integral, so if the boundary atmospheric condition at the horizon are determined, the state of the field outside volition be specified. To discover the appropriate boundary conditions, consider a stationary observer but exterior the horizon at position

${\displaystyle r=2M+{\frac {\rho ^{ii}}{8M}}\,.}$

The local metric to lowest order is

${\displaystyle \left(\mathrm {d} s\right)^{2}\;=\;-\left({\frac {\rho }{4M}}\right)^{two}\,\left(\mathrm {d} t\right)^{2}+\left(\mathrm {d} \rho \right)^{two}+\left(\mathrm {d} X_{\perp }\right)^{ii}\;=\;-\rho ^{ii}\,\left(\mathrm {d} \tau \correct)^{2}+\left(\mathrm {d} \rho \right)^{2}+\left(\mathrm {d} X_{\perp }\correct)^{2}}$ ,

which is Rindler in terms of τ = t / ivGrand . The metric describes a frame that is accelerating to go on from falling into the blackness pigsty. The local acceleration, α = i / ρ , diverges as ρ → 0.

The horizon is non a special boundary, and objects can fall in. And 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

${\displaystyle T\;=\;{\frac {\alpha }{2\pi }}\;=\;{\frac {1}{2\pi \rho }}\;=\;{\frac {1}{4\pi {\sqrt {2Mr\left(1-{\frac {2M}{r}}\right)\,}}\,}}\,}$ ;

which is the Unruh result.

The gravitational redshift is given by the square root of the fourth dimension component of the metric. So for the field theory state to consistently extend, in that location must be a thermal groundwork everywhere with the local temperature redshift-matched to the virtually horizon temperature:

${\displaystyle T(r')\;=\;{\frac {ane}{\,iv\pi {\sqrt {2Mr\left(1-{\frac {2M}{r}}\correct)\,}}\,}}{\sqrt {\frac {one-{\frac {2M}{r}}}{\,1-{\frac {2M}{r'}}\,}}}\;=\;{\frac {1}{4\pi {\sqrt {2Mr\left(1-{\frac {2M}{r'}}\right)}}}}\,}$ .

The inverse temperature redshifted to r′ at infinity is

${\displaystyle T(\infty )={\frac {1}{4\pi {\sqrt {2Mr}}}}}$

and r is the near-horizon position, about 2M , so this is really:

${\displaystyle T(\infty )={\frac {i}{eight\pi M}}}$ .

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

${\displaystyle T_{\text{H}}={\frac {one}{8\pi M}}}$ .

This can be expressed in a cleaner style in terms of the surface gravity of the blackness hole; this is the parameter that determines the dispatch of a near-horizon observer. In Planck units ( M = c = ħ = k _B = one), the temperature is

${\displaystyle T_{\text{H}}={\frac {\kappa }{2\pi }}}$ ,

where κ is the surface gravity of the horizon (in units of lightspeed per Planck-time squared). And so a blackness hole can only exist in equilibrium with a gas of radiation at a finite temperature. Since radiation incident on the black pigsty is absorbed, the blackness hole must emit an equal amount to maintain detailed balance. The blackness hole acts every bit a perfect blackbody radiating at this temperature.

In SI units, the radiation from a Schwarzschild blackness hole is blackbody radiation with temperature

${\displaystyle T={\frac {\hbar \,c^{3}}{8\pi Gk_{\text{B}}One thousand}}\;\approx \;one.2\times x^{23}{\text{1000}}\,\times {\frac {1\,{\text{kg}}}{M}}\;=\;6\times 10^{-viii}{\text{One thousand}}\,\times {\frac {M_{\odot }}{M}}\,}$ ,

where ħ is the reduced Planck abiding, c is the speed of light, g _B is the Boltzmann constant, G is the gravitational abiding, M _☉ is the solar mass, and M is the mass of the black hole.

Without loss of generality the radiation formula can be further reduced to

${\displaystyle T={\frac {T_{\text{P}}}{2{\pi }d}}}$ ,

where ${\displaystyle d}$ is the existent multiplier of the blackness hole diameter ${\displaystyle D=dl_{\text{P}}}$ , where ${\displaystyle l_{\text{P}}}$ is Planck length and ${\displaystyle T_{\text{P}}}$ is Planck temperature. Solving the Hawking temperature for the blackness hole surface gravity ${\displaystyle g={\frac {GM}{R^{two}}}={\frac {G}{R^{2}}}{\frac {Rc^{ii}}{2G}}={\frac {c^{2}}{2R}}={\frac {c^{2}}{D}}}$ , it tin can exist expressed as

${\displaystyle g={\frac {2\pi ck_{\mathrm {B} }}{\hbar }}T=2\pi a_{\mathrm {P} }{\frac {T}{T_{\mathrm {P} }}}={\frac {a_{\mathrm {P} }}{d}}}$ ,

where ${\displaystyle a_{\mathrm {P} }}$ is Planck acceleration.

From the black hole temperature, information technology is straightforward to summate the black hole entropy Southward. The alter in entropy when a quantity of estrus dQ is added is:

${\displaystyle \mathrm {d} S\;=\;{\frac {\mathrm {d} Q}{T}}\;=\;8\pi Grand\,\mathrm {d} Q\,}$ .

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

${\displaystyle \mathrm {d} South\;=\;viii\pi M\,\mathrm {d} M\;=\;\mathrm {d} \left(4\pi Grand^{two}\right)\,}$ .

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

${\displaystyle S=\pi R^{2}={\frac {A}{4}}}$ .

Assuming that a pocket-size blackness pigsty has zero entropy, the integration constant is nada. Forming a black pigsty is the nigh efficient way to compress mass into a region, and this entropy is likewise a spring on the information content of whatever sphere in space time. The grade of the upshot strongly suggests that the physical description of a gravitating theory tin be somehow encoded onto a bounding surface.

Black pigsty evaporation [edit]

When particles escape, the blackness pigsty loses a small amount of its energy and therefore some of its mass (mass and energy are related by Einstein's equation E = mc ⁱⁱ ). Consequently, an evaporating black hole will have a finite lifespan. By dimensional analysis, the life span of a black hole tin can be shown to calibration as the cube of its initial mass,^{[sixteen] [17] : 176–177} and Hawking estimated that any black hole formed in the early universe with a mass of less than approximately ten¹⁵ g would have evaporated completely past the present day.^[xviii]

In 1976, Don Page refined this estimate by calculating the power produced, and the time to evaporation, for a nonrotating, not-charged Schwarzschild black hole of mass Thou.^[xvi] The time for the event horizon or entropy of a black hole to halve is known every bit the Page time.^[19] The calculations are complicated by the fact that a black pigsty, beingness of finite size, is non a perfect black body; the assimilation cross section goes down in a complicated, spin-dependent manner as frequency decreases, particularly when the wavelength becomes comparable to the size of the result horizon. Page concluded that primordial black holes could only survive to the nowadays day if their initial mass were roughly 4×x^xi 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 ii neutrino flavors be, and therefore his results of blackness hole lifetimes do not lucifer the modern results which take into account 3 flavors of neutrinos with nonzero masses. A 2008 adding using the particle content of the Standard Model and the WMAP figure for the age of the universe yielded a mass spring of (5.00±0.04)×10^xi kg.^[20]

If black holes evaporate nether Hawking radiation, a solar mass black pigsty will evaporate over 10⁶⁴ years which is vastly longer than the age of the universe.^[21] A supermassive blackness hole with a mass of ten¹¹ (100 billion) G _☉ will evaporate in around two×10¹⁰⁰ years.^[22] Some monster black holes in the universe are predicted to continue to grow upwardly to perchance 10¹⁴ K _☉ during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of upwardly to x¹⁰⁶ years.^[21]

The power emitted by a black hole in the form of Hawking radiation can easily exist estimated for the simplest instance of a nonrotating, non-charged Schwarzschild blackness pigsty of mass M. Combining the formulas for the Schwarzschild radius of the black hole, the Stefan–Boltzmann police force 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'due south consequence horizon), several equations can exist derived.

The Hawking radiation temperature is:^{[4] [23] [24]}

${\displaystyle T_{\mathrm {H} }={\frac {\hbar c^{three}}{eight\pi GMk_{\mathrm {B} }}}}$

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:^{[24] [23]}

${\displaystyle P={\frac {\hbar c^{half dozen}}{15360\pi Thou^{2}K^{2}}}}$

where P is the luminosity, i.east., the radiated power, ħ is the reduced Planck abiding, c is the speed of low-cal, G is the gravitational constant and 1000 is the mass of the black hole. Information technology is worth mentioning that the above formula has non yet been derived in the framework of semiclassical gravity.

The fourth dimension that the black pigsty takes to dissipate is:^{[24] [23]}

${\displaystyle t_{\mathrm {ev} }={\frac {5120\pi G^{two}M^{3}}{\hbar c^{four}}}={\frac {480c^{ii}V}{\hbar K}}\approx 2.i\times 10^{67}\,{\text{years}}\ \left({\frac {M}{M_{\odot }}}\right)^{iii},}$

where Grand and V are the mass and (Schwarzschild) volume of the black pigsty. A black hole of one solar mass ( Grand _☉ = two.0×10³⁰ kg) takes more x⁶⁷ years to evaporate—much longer than the electric current age of the universe at 1.4×ten^ten years.^[25] But for a black hole of 10¹¹ kg, the evaporation time is ii.half-dozen×10⁹ years. This is why some astronomers are searching for signs of exploding primordial black holes.

Withal, since the universe contains the cosmic microwave background radiation, in order for the blackness pigsty to dissipate, the black hole must have a temperature greater than that of the present-day blackbody radiation of the universe of 2.vii One thousand. In 2020, Chou proposed a theory that if a rotating radiating primordial black hole has a mass similar to Pluto, its Hawking radiation temperature will be 9.42 Chiliad, higher than 2.7 K CMB.^[26] Some other study suggests that Thousand must exist less than 0.8% of the mass of the Globe^[27] – approximately the mass of the Moon.

Blackness hole evaporation has several significant consequences:

• Black pigsty evaporation produces a more consistent view of black hole thermodynamics by showing how black holes interact thermally with the residuum of the universe.
• Different most objects, a blackness pigsty's temperature increases as it radiates away mass. The charge per unit of temperature increase is exponential, with the most likely endpoint beingness the dissolution of the black hole in a violent burst of gamma rays. A complete description of this dissolution requires a model of quantum gravity, however, as it occurs when the black pigsty's mass approaches i Planck mass, when its radius will besides approach two Planck lengths.
• The simplest models of blackness pigsty evaporation lead to the black hole information paradox. The data content of a black pigsty appears to be lost when information technology dissipates, as under these models the Hawking radiations 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 exist lost under these atmospheric condition.

Problems and extensions [edit]

Trans-Planckian problem [edit]

The trans-Planckian problem is the issue that Hawking'southward original calculation includes quantum particles where the wavelength becomes shorter than the Planck length most the black pigsty'southward horizon. This is due to the peculiar behavior there, where fourth dimension stops as measured from far abroad. 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 trans-Planckian wavelength.

The Unruh effect and the Hawking effect both talk nigh field modes in the superficially stationary spacetime that change frequency relative to other coordinates that are regular across the horizon. This is necessarily and then, since to stay outside a horizon requires acceleration that constantly Doppler shifts the modes.^{[ citation needed ]}

An approachable photon of Hawking radiation, if the mode is traced back in time, has a frequency that diverges from that which information technology has at neat distance, as it gets closer to the horizon, which requires the wavelength of the photon to "scrunch up" infinitely at the horizon of the blackness hole. In a maximally extended external Schwarzschild solution, that photon'southward frequency stays regular only if the style is extended back into the by region where no observer can go. That region seems to exist unobservable and is physically doubtable, then Hawking used a black pigsty solution without a past region that forms at a finite time in the past. In that case, the source of all the outgoing photons tin exist identified: a microscopic signal right at the moment that the black hole first formed.

The quantum fluctuations at that tiny point, in Hawking's original calculation, incorporate all the outgoing radiation. The modes that eventually comprise the outgoing radiation at long times are redshifted past such a huge amount by their long sojourn next to the event horizon that they commencement off every bit modes with a wavelength much shorter than the Planck length. Since the laws of physics at such short distances are unknown, some discover Hawking's original calculation unconvincing.^{[28] [29] [30] [31]}

The trans-Planckian trouble is nowadays generally 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, merely has no time to come region into which it tin can become. Tracing the futurity 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 indicate of view of outside coordinates are atypical in frequency there. The only way to determine what happens classically is to extend in some other coordinates that cross the horizon.

In that location exist alternative physical pictures that requite the Hawking radiation in which the trans-Planckian problem is addressed.^{[ citation needed ]} The fundamental signal is that similar trans-Planckian problems occur when the modes occupied with Unruh radiations are traced back in time.^[14] In the Unruh effect, the magnitude of the temperature tin be calculated from ordinary Minkowski field theory, and is non controversial.

[edit]

The formulae from the previous department are applicative but if the laws of gravity are approximately valid all the way down to the Planck scale. In item, for blackness holes with masses below the Planck mass (~ 10⁻⁸ kg), they outcome 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 blackness hole.

In a model with large extra dimensions (x or xi), the values of Planck constants can be radically dissimilar, and the formulae for Hawking radiations take to be modified too. In item, the lifetime of a micro black hole with a radius below the scale of the extra dimensions is given past equation ix in Cheung (2002)^[32] and equations 25 and 26 in Carr (2005).^[33]

${\displaystyle \tau \sim {\frac {ane}{M_{*}}}\left({\frac {M_{\mathrm {BH} }}{M_{*}}}\right)^{\frac {north+3}{n+1}}\,,}$

where M _∗ is the low energy scale, which could be as low every bit a few TeV, and n is the number of large extra dimensions. This formula is at present consistent with black holes every bit light as a few TeV, with lifetimes on the order of the "new Planck fourth dimension" ~ ten⁻²⁶ southward.

In loop breakthrough gravity [edit]

A detailed study of the quantum geometry of a black hole event horizon has been made using loop quantum gravity.^{[34] [35]} Loop-quantization does not reproduce the consequence for blackness hole entropy originally discovered by Bekenstein and Hawking, unless the value of a free parameter is gear up to abolish out diverse constants such that the Bekenstein-Hawking entropy formula is reproduced. However, quantum gravitional 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 blackness pigsty exhibits deviations from the Hawking spectrum that would be observable were X-rays from Hawking radiation of evaporating primordial black holes to be observed.^[36] The quantum effects are centered at a set of discrete and unblended frequencies highly pronounced on tiptop of Hawking radiation spectrum.^[37]

Experimental observation [edit]

Astronomical search [edit]

In June 2008, NASA launched the Fermi space telescope, which is searching for the terminal gamma-ray flashes expected from evaporating primordial black holes.

Heavy-ion collider physics [edit]

If speculative large extra dimension theories are correct, then CERN's Big Hadron Collider may be able to create micro black holes and discover their evaporation. No such micro blackness pigsty has been observed at CERN.^{[38] [39] [40] [41]}

Experimental [edit]

Under experimentally achievable conditions for gravitational systems, this effect is too modest to be observed straight. It was predicted 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 catamenia of an approximately perfect fluid is analogous to gravity (see Analog models of gravity).^[42] Observations of Hawking radiation were reported, in sonic black holes employing Bose-Einstein condensates.^{[43] [44] [45]}

In September 2010 an experimental prepare-up created a laboratory "white hole event horizon" that the experimenters claimed was shown to radiate an optical analog to Hawking radiations.^[46] However, the results remain unverified and debatable,^{[47] [48]} and its status as a genuine confirmation remains in doubt.^[49]

See also [edit]

• Black hole thermodynamics
• Blackness hole starship
• Blandford–Znajek process and Penrose process, other extractions of black-hole energy
• Gibbons–Hawking effect
• Thorne–Hawking–Preskill bet
• Unruh effect

References [edit]

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21. ^ ^{a b} See page 596: tabular array i and the "blackness pigsty 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. S2CID 27717447. Since we have causeless a maximum scale of gravitational binding – for instance, superclusters of galaxies – black pigsty formation somewhen comes to an end in our model, with masses of upward to 10¹⁴ One thousand _☉ ... the timescale for black holes to radiate away all their energy ranges from to ten⁶⁴ years for black holes of i solar mass ...
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23. ^ ^{a b c} Hawking Radiation Calculator
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Further reading [edit]

• Hawking, Stephen W. (1974). "Black hole explosions?". Nature. 248 (5443): 30–31. Bibcode:1974Natur.248...30H. doi:ten.1038/248030a0. S2CID 4290107. → Hawking's first article on the topic
• Page, Don Northward. (1976). "Particle emission rates from a black pigsty: Massless particles from an uncharged, nonrotating hole". Concrete 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 Due west. (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:ten.1093/mnras/168.ii.399. → links betwixt primordial blackness holes and the early universe
• Barrau, Aurélien; et al. (2002). "Antiprotons from primordial black holes". Astronomy & Astrophysics. 388 (2): 676–687. arXiv:astro-ph/0112486. Bibcode:2002A&A...388..676B. doi:x.1051/0004-6361:20020313. S2CID 17033284.
• Barrau, Aurélien; et al. (2003). "Antideuterons as a probe of primordial blackness holes". Astronomy & Astrophysics. 398 (2): 403–410. arXiv:astro-ph/0207395. Bibcode:2003A&A...398..403B. doi:10.1051/0004-6361:20021588. S2CID 5727582.
• Barrau, Aurélien; Féron, Chloé; Grain, Julien (2005). "Astrophysical Production of Microscopic Black Holes in a Low-Planck-Scale World". The Astrophysical Journal. 630 (2): 1015–1019. arXiv:astro-ph/0505436. Bibcode:2005ApJ...630.1015B. doi:10.1086/432033. S2CID 6411086. → experimental searches for primordial black holes thanks to the emitted antimatter
• Barrau, Aurélien; Boudoul, Gaëlle (2002). "Some aspects of primordial black hole physics". arXiv:astro-ph/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 infinite". Physics Letters B. 584 (1–2): 114–122. arXiv:hep-ph/0311238. Bibcode:2004PhLB..584..114B. doi:ten.1016/j.physletb.2004.01.019. S2CID 14275281. → searches for new physics (quantum gravity) with primordial blackness holes
• Kanti, Panagiota (2004). "Black Holes in Theories with Large Extra Dimensions: a Review". International Journal of Modern Physics A. xix (29): 4899–4951. arXiv:hep-ph/0402168. Bibcode:2004IJMPA..19.4899K. doi:ten.1142/S0217751X04018324. S2CID 11863375. → evaporating black holes and extra-dimensions
• Ida, Daisuke; Oda, Kin'ya; Park, Seong-chan (2003). "Rotating black holes at future colliders: Greybody factors for brane fields". Physical Review D. 67 (6): 064025. arXiv:hep-th/0212108. Bibcode:2003PhRvD..67f4025I. doi:ten.1103/PhysRevD.67.064025.
• Ida, Daisuke; Oda, Kin'ya; Park, Seong-chan (2005). "Rotating black holes at future colliders. Ii. Anisotropic scalar field emission". Concrete Review D. 71 (12): 124039. arXiv:hep-thursday/0503052. Bibcode:2005PhRvD..71l4039I. doi:10.1103/PhysRevD.71.124039. S2CID 28276606.
• Ida, Daisuke; Oda, Kin'ya; Park, Seong-chan (2006). "Rotating Black Holes at Future Colliders. 3. Determination of Black Pigsty Development". Concrete Review D. 73 (12): 124022. arXiv:hep-th/0602188. Bibcode:2006PhRvD..73l4022I. doi:10.1103/PhysRevD.73.124022. S2CID 6702415. → 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:10.1088/0305-4470/36/27/317. → consistent derivation of the Hawking radiation in the Fulling–Davies mirror model.
• Smolin, Lee (Nov 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 x, 2008. consists of the recent developments and predictions of loop breakthrough gravity nigh gravity in small scales including the departure from Hawking radiation result by Ansari.
• Ansari, Mohammad H. (2007). "Spectroscopy of a canonically quantized horizon". Nuclear Physics B. 783 (three): 179–212. arXiv:hep-th/0607081. Bibcode:2007NuPhB.783..179A. doi:10.1016/j.nuclphysb.2007.01.009. S2CID 9966483. → studies the deviation of a loop quantized black hole from Hawking radiations. 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 . Wiley-Interscience. p. 366. ISBN978-0-471-87316-7. → Hawking radiation evaporation formula derivation.
• Leonhardt, Ulf; Maia, Clovis; Schuetzhold, Ralf (2010). "Focus on Classical and Breakthrough Analogs for Gravitational Phenomena and Related Effects". New Journal of Physics . fourteen (ten): 105032. Bibcode:2012NJPh...14j5032L. doi:x.1088/1367-2630/14/10/105032.

External links [edit]

• Hawking radiation calculator tool
• The case for mini blackness holes A. Barrau & J. Grain explain how the Hawking radiation could be detected at colliders

rauchhatint.blogspot.com

Source: https://en.wikipedia.org/wiki/Hawking_radiation

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