Black-Hole
Radiation| Black-Hole
Radiation |
In General > s.a. equivalence
principle; quantum field theory
in curved spacetime; quantum
black holes.
* Idea: An equilibrium
black hole emits thermal radiation corresponding to a temperature TH;
An instance of a purely kinematic result from quantum field theory in a curved
background Lorentzian geometry
containing an event horizon,
stating
that certain observers will detect a thermal particle state, with temperature
depending
on horizon properties; In the black-hole case, it is interpreted
by relaxing
the energy conditions that would forbid negative energy particles
and a decrease of black-hole area, and one concludes that a black hole can
radiate energy by creating
in its field particle-antiparticle pairs, and swallowing the negative
energy
particles.
* Transplanckian issue:
Because of the infinite gravitational redshift, Hawking quanta emerge from
configurations
with ultra-high (trans-Planckian) frequencies
at
the event horizon; Therefore Hawking radiation cannot be derived within
a low-energy effective theory, and all derivations make some assumptions
concerning Planck scale physics.
* Precursors: Acceleration
radiation (Davies), spontaneous radiation from rotation (Unruh).
* Evaporation time: As
a consequence of the radiation, a black hole evaporates in a time tH 
2560
M 3/Nf
=
640 NBM/Nf,
where Nf = effective number
of distinct radiated field modes, and NB:=
4M2/ the
Bekenstein number, equal
to the entropy for non-rotating black holes.
Special Effects / Properties of Emitted Radiation > s.a.
black holes and information; entropy
bounds [hyperentropic]; quantum black holes.
* Nature of radiation:
Quanta of all fields that couple to the geometry and to any charges the black
hole may have are radiated; In 4D, for T greater than all particle
masses, and using standard model parameters, Page estimated that 1.8% of the
energy
is radiated in scalar particles, 88% in fermions, 9.8% in vectors, and 0.1%
in gravitons; In higher dimensions, the gravitational contribution
increases.
* Spectrum: Various authors
have proposed that it is not exactly thermal, due to (i) Frequency-dependent
greybody factors in the potential barrier, (ii) Dynamical nature of black-hole
background and energy conservation, back-reaction, in the tunneling approach,
or (iii) Quantum correlations.
@ Rates and spectra: Page PRD(76),
PRD(76), & Hawking AJ(76);
Maldacena & Strominger PRD(97)ht/96 [D-branes];
Daghigh & Lapusta PRD(06)
[microscopic black holes, p and anti-p]; Boonserm & Visser
PRD(08)-a0806 [bounds
on greybody factors]; Greenwood & Stojkovic JHEP(09) [as seen by infalling
observers]; > s.a. Greybody
Factor.
@ Stimulated emission: Bekenstein & Meisels PRD(77); Panangaden & Wald
PRD(77).
@ Entropy: Bekenstein PRD(75);
Kundt Nat(76)jan.
@ Back-reaction: Balbinot CQG(84);
York in(84); Balbinot & Barletta CQG(89);
Kraus gq/95-PhD;
Zaidi & Gegenberg PRD(98)gq/97;
Massar & Parentani
gq/98, NPB(00)gq/99;
Hu et al gq/99-in;
Fabbri et al GRG(01)gq/01,
NPB(02)ht/01 [and
info paradox]; Ring ht/05 [evaporation
rate suppression]; Vilkovisky PLB(06);
Maia & Schützhold PRD(07) [toy model].
@ Quantum-gravity effects, metric fluctuations: Barrabès et al PRD(99);
Wu & Ford
PRD(99)gq;
Jacobson gq/01-in
[and Lorentz violation]; Parentani IJTP(02)-a0705;
Agulló et al PRL(06), PRD(07)
[short-distance physics]; Thompson & Ford PRD(08)-a0803;
Schützhold & Unruh PRD(08)-a0805,
Barceló et al PRD(09)-a0807 [modified
dispersion relations]; Husain & Mann CQG-a0812 [phase
transition and no radiation near Planck scale]; Nicolini & Rinaldi a0910 [and
minimal length].
@ Related topics: Jacobson & Kang CQG(93)gq [conformal
invariance of T]; 't Hooft NPPS(98)gq/97 [description
as effective matter envelope];
Helfer PLA(04)gq [detection
and energy extraction]; Dai & Stojkovic PRD-a0812 [unparticles];
Nowakowski & Arraut a0905 [minimum
and maximum temperature]; > s.a. dark-energy
models; gravitational
instantons; types of black holes.
Different Approaches and Situations > s.a. black
holes in modified theories [2D]; kerr-newman
solutions.
@ And path-integral quantum gravity: Hartle & Hawking PRD(76);
York & Schmekel PRD(05).
@ And loop quantum gravity: Ashtekar & Bojowald CQG(05)gq [dynamical
horizons]; Díaz-Polo & Fernández-Borja CQG(08)-a0706 [isolated
horizons].
@ Derivations / models: Gerlach PRD(76)
[incipient black hole]; Lapedes PRD(78)
[euclidean formalism]; Kraus & Wilczek MPLA(94);
Parentani & Piran PRL(94)ht;
Scardigli NCB(95)gq/02;
Visser IJMPD(03)ht/01 [essential
features]; Melnikov & Weinstein ht/01,
Weinstein NPPS(02)gq/01-in, ht/02-in
[Hamiltonian]; Canfora & Vilasi gq/03 [and
trace anomaly]; Kiefer CQG(04)gq [and
quasi-normal modes]; Yu & Zhang PRD(08)-a0806 [as
open quantum system]; Peltola CQG(09)-a0807 [local
approach].
@ As tunneling: Berezin et al G&C(99)gq/06;
Parikh & Wilczek PRL(00)ht/99;
Parikh GRG(04)ht-GRF;
Angheben et al JHEP(05)
[extremal and rotating]; Medved & Vagenas MPLA(05)gq;
Arzano et al JHEP(05)ht;
Liu gq/05;
Jiang et al PRD(06)ht/05 [rotating];
Ren et al GRG(06)
[with topological defects]; Hu et al gq/06 [and
laws of black-hole dynamics]; Kerner & Mann PRD(06)gq [Taub-NUT];
Wu & Jiang JHEP(06)
[BTZ black holes]; Pilling PLB(08)-a0709 [and
first law]; Banerjee & Majhi JHEP(08)
[beyond the semiclassical approximation]; Stotyn et al CQG-a0811 [coordinate-free
formulation].
@ Gravitational anomalies approach: Robinson & Wilczek PRL(05)gq;
Das et al IJMPD(08)-a0705;
Chen & He a0705;
Banerjee & Kulkarni PRD(08)-a0707;
Peng & Wu a0708-wd
[counterexample]; Wu et al CQG(08)-a0803;
Akhmedova et al PLB-a0808 [comment];
Banerjee IJMPD(09)-a0807 [GRF];
Morita
PLB(09)
[2D conformal field theory method]; > s.a. black-hole
analogs.
References > s.a. black
holes; black-hole phenomenology; Superradiance.
@ Reviews: Traschen gq/00-in;
Helfer RPP(03)gq [critical];
Page NJP(05)ht/04-in, ht/06-in.
@ General: Hawking Nat(74)mar
[announcement], CMP(75)
[original proposal], in(75); Davies JPA(75)
[hint from acceleration radiation]; Wald CMP(75);
Unruh PRD(76);
Hawking PRD(76),
SA(77)jan; Unruh PRD(77);
Hájícek & Israel PLA(80);
Sewell PLA(80)
[rigorous, interacting fields]; York PRD(83);
Kay in(86); Carlitz & Willey PRD(87);
Kay & Wald in(87); Akhmedov et al IJMPD(09)-a0805 [correct
semiclassical calculation].
@ Interpretations: Raval et al PRD(97)gq/96;
Visser PRL(98)gq/97;
Gupta & Sen PLB(03)ht/02 [geodesic
motion on black-hole space].
@ Origin: Boulware PRD(76);
Hájícek PRD(87);
Biernacki CQG(89);
Jacobson PRD(96)ht; Kiefer CQG(01)gq [decoherence];
Unruh & Schützhold PRD(05)gq/04 [and
Planck-scale physics].
@ Related topics: Bowick et al GRG(87)
[and strings]; Moffat gq/93 [predictability];
Visser MPLA(93)
[black holes as decaying particles]; Verlinde ht/95-in
[complementarity]; Visser PRL(98)gq/97 [without
black-hole thermodynamics]; Corley & Jacobson PRD(98)ht/97 [lattice
version]; Parentani PRD(00)gq/99 [and
scattering]; Goncharov & Firsova PLB(00)ap;
Materassi JHEP(00)ht [conformal
nature]; Shankaranarayanan et al MPLA(01)
[general covariance]; Casadio CQG(02)ht/01 [dispersion
relations]; Valentini ht/04 [and
hidden variables]; Saida CQG(06)gq, CQG(07)gq,
a0711-in [as
non-equilibrium process]; Yu & Zhou PRD(07)-a0707 [spontaneous
excitation of atoms]; Banerjee & Kulkarni PLB(08)
[from effective action and
covariant boundary conditions]; McInnes NPB(09)
[unitarity and conspiracies]; > s.a. Ergosphere.
Arguments for Modified or No Radiation / Evaporation
* T D Lee 1986: Argued
that the thermal state is a consequence of a particular choice of state; But,
contrary
to what he says, it will show up,
no matter what state we start with (see also "no hair" theorems),
and we cannot have access to information from inside a black hole (we can if
somehow we knew already what went inside it).
* A Helfer 2000: Black-hole
radiation is suppressed by quantum back-reaction effects on matter, and thus
on black-hole geometry, that set in even at lower energies
than
the ones involved in black-hole radiation calculations.
@ No radiation / evaporation: Lee NPB(86);
Belinski PLA(95);
Helfer gq/00,
RPP(03)gq;
Sivaram GRG(01)
[in practice]; Nikolic IJMPD(05)ht/04;
Chavda & Chavda
phy/04 [assumes
equilibrium!]; Belinski PLA(06)gq.
@ Non-thermal spectrum: Parikh ht/04 [energy
conservation]; Dai & Liu LMP(07) [massive particles].
"Since black holes behave like black bodies, they are not black" – S W Hawking
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16 oct 2009