Black-Hole Radiation |

**In General** > s.a. black holes and information;
quantum field theory in curved spacetime.

* __Idea__: An
equilibrium black hole emits thermal radiation corresponding to a
temperature *T*_{H}; This is 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.

* __Mechanism__: In the
black-hole case, the current evaporation scenario holds that the Hawking
energy flux is powered by pair creation at the horizon; The radiation 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.

* __History__:
Precursors were P Davies' acceleration radiation, and W Unruh's
spontaneous radiation from rotation.

* __Evaporation time__:
As a consequence of the radiation, a black hole evaporates in a time *t*_{H}
~ 2560π*M*^{ 3}/*N*_{f}\(\hbar\)
= 640 *N*_{B}*M*/*N*_{f},
where *N*_{f} = effective number of
distinct radiated field modes, and *N*_{B}:=
4π*M*^{2}/\(\hbar\) the Bekenstein
number, equal to the entropy for non-rotating black holes.

__Related topics__: see black-hole
analogs; phenomenology and approaches;
radiation from quantum black holes [and
quantum gravity effects]; unruh effect.

**References** > s.a. black holes;
black-hole phenomenology; thermodynamics
for different types of black holes.

@ __Reviews__: Traschen gq/00-ln;
Helfer RPP(03)gq [critical];
Page NJP(05)ht/04-in,
ht/06-MGXI;
Jacobson ch(13)-a1212-ln,
Lambert a1310-PoS [intro].

@ __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);
Hájíček & Israel PLA(80);
York PRD(83);
Kay in(86);
Carlitz & Willey PRD(87);
Kay & Wald in(87); Akhmedov et al IJMPD(09)-a0805 [correct semiclassical calculation];
Barceló et al PRD(11)-a1011 [horizon not necessary for the existence of a Hawking-like flux];
Barbado et al CQG(11)-a1101,
CQG(12),
AIP(12)-a1203 [as perceived by different observers];
Brustein & Medved JHEP(14)-a1312 [horizons of semiclassical black holes are cold];
Unruh FP(14) [Hawking radiation has been measured and shown to possess a thermal spectrum];
Visser JHEP(15)-a1410 [thermality and correlations];
Ho JHEP(15)-a1505 [comment on self-consistent model];
Brustein et al a1707 [the state is non-classical].

@ __Interacting fields__: Sewell PLA(80) [rigorous]; Frasca EPJP(17)-a1412.

@ __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);
Hájíček PRD(87);
Biernacki CQG(89);
Jacobson PRD(96)ht;
Kiefer CQG(01)gq [decoherence];
Unruh & Schützhold PRD(05)gq/04 [and Planck-scale physics];
Kim GRG(17)-a1604 [firewall or atmosphere?];
Hod PLB(16)-a1607 [effective quantum atmosphere];
Barbado et al JHEP(16)-a1608 [Hawking versus Unruh effect];
Dey et al PLB(17)-a1701 [black-hole quantum atmosphere].

@ __Unitarity__: McInnes NPB(09) [and conspiracies];
't Hooft FP(16)-a1601 [and antipodal entanglement].

@ __Dispersion relations__: Casadio CQG(02)ht/01;
Coutant & Parentani PRD(14)-a1402 [with high-frequency dispersion].

@ __Approaches__: Bowick et al GRG(87) [and strings];
Visser PRL(98)gq/97 [without black-hole thermodynamics];
Corley & Jacobson PRD(98)ht/97 [lattice version];
Banerjee & Kulkarni PLB(08) [from effective action and covariant boundary conditions];
Barman et al PRD(18)-a1707 [canonical derivation].

@ __Related topics__: Moffat gq/93 [predictability];
Visser MPLA(93) [black holes as decaying particles];
Verlinde ht/95-ln [complementarity];
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];
Valentini ht/04 [and hidden variables];
Saida CQG(06)gq,
CQG(07)gq,
a0711-proc [as non-equilibrium process];
Yu & Zhou PRD(07)-a0707 [spontaneous excitation of atoms];
Bellucci & Tiwari JHEP(10)-a1009 [thermodynamic geometry and fluctuations];
Almheiri et al JHEP(13)-a1207 [complementarity or firewalls?];
Braunstein & Pirandola a1311
[leaky horizons or exotic atmospheres];
Corda CQG(15)-a1411 [and the tunneling mechanism];
Mück EPJC(16)-a1606 [total number of emitted quanta].

> __Related topics__:
see black holes and information [endpoint, remnant];
Ergosphere; Superradiance;
Zitterbewegung.

**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];
Nikolić IJMPD(05)ht/04;
Chavda & Chavda phy/04 [assumes equilibrium!];
Belinski PLA(06)gq;
Yi JCAP(11);
Ellis a1310 [radiation, but no evaporation];
Nikolić PLB(14)-a1311 [suppression by the quantum Zeno effect].

@ __Non-thermal spectrum__: Parikh ht/04 [energy conservation];
Dai & Liu LMP(07)

"Since black holes behave like black bodies, they are not black" – S W Hawking

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