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 TH; 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.
* Trans-planckian issue: Because of the infinite gravitational redshift, Hawking quanta emerge from configurations with ultrahigh (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 Paul 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 tH ~ 2560π M 3/Nf\(\hbar\) = 640 NBM/Nf, where Nf = effective number of distinct radiated field modes, and NB:= 4π M2/\(\hbar\) the Bekenstein number, equal to the entropy for non-rotating black holes.
blue bullet 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 JHEP(18)-a1707 [the state is non-classical].
@ Types of fields: Sewell PLA(80) [interacting, axiomatic field theory]; Frasca EPJP(17)-a1412 [interacting]; Kajuri & Kothawala PLB(19)-a1806 [non-local].
@ 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]; Banerjee & Kulkarni PLB(08) [from effective action and covariant boundary conditions]; Barman et al PRD(18)-a1707 [canonical derivation]; Övgün & Sakallı AP(20)-a1902 [topological method, Gauss-Bonnet theorem]; > s.a. phenomenology [computational].
@ Quantum gravity corrections: Eyheralde et al CQG(20)-a1908 [quantum geometry fluctuations]; Flanagan a2102 [and the information loss paradox]
@ 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]; Ghosh a1901 [more general spacetimes]; Banerjee & Majhi EPJC(20)-a1909 [and Kubo's fluctuation-dissipation relation]; Aurell et al a2012 [quantum information]; > s.a. Ergosphere; Superradiance; Zitterbewegung.
> Endpoint of evaporation: see black holes and information [endpoint, remnant]; quantum black hole radiation [transition to white hole].

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 MGX(06)-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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