Quantum Black-Hole Radiation / Spectrum  

In General {& V Mukhanov, GE seminar 24.11.1995.} > s.a. quantum black holes [entropy].
* Discrete, equal spacing: (Bekenstein & Mukhanov) A = 4 ln 2, where n is a principal quantum number, of degeneracy Γ = 2 n–1 (from S ~ ln Γ and S = A/4), so M ~ n1/2; Lifetime of a level τ ~ 3840 γ–1 M ln2, γ ~ 1; (Hod) A = 4n\(\hbar\)/ln3; This kind of spectrum is not consistent with loop quantum gravity.
@ Area quantization, quantum geometry: Louko & Mäkelä PRD(96)gq; Hod PRL(98)gq; Kastrup AdP(00)gq/99; Ashtekar et al ATMP(00)gq/00 [isolated horizons]; Khriplovich PLB(02)gq/01, gq/02-conf; Kunstatter PRL(03)gq/02; Abdalla et al MPLA(03)gq [quasi-extremal]; Gegenberg et al CQG(06)gq [midi-superspace approach].
@ Radiation, in lqg: Ansari NPB(07)ht/06; Díaz-Polo & Fernández-Borja CQG(08)-a0706; Geiller & Noui a1402 [near-horizon radiation]; Gambini & Pullin CQG(14)-a1402; Gambini & Pullin a1408 [Schwarzschild, scenario]; Barrau et al PRD(15)-a1504 [spectra from Monte Carlo simulations], a1605 [possible line spectrum].
@ Spectrum: Jacobson PRD(91), PRD(93)ht; Louko & Whiting CQG(92); Loustó PLB(95)gq/94; Maggiore NPB(94)gq; Unruh PRD(95)gq/94 [acoustic analogs]; Verlinde ht/95-ln; Krasnov CQG(99)gq/97; Berezin et al PLB(99)gq/98, G&C(99); Berezin IJMPA(02)gq/01-conf; Khriplovich gq/04-conf [and correspondence], IJMPD(05) [and quasinormal modes]; Das et al CQG(05)ht/04 [rotating, any dimension]; Setare ht/05-ch; Parwani IJMPA(09)-a0904-conf [corrections to equispaced spectrum]; Medved MPLA(09)-a0906, Ropotenko PRD(09) [equal spacing]; Mania & Maziashvili PLB(11) [and minimum-length deformed quantization].
@ Continuous spectrum: Cavaglià et al IJMPD(95)gq/94, IJMPD(96)gq/95; Barreira et al GRG(96)gq; Mäkelä PLB(97)gq/96; Hollmann JMP(98)gq/96; Nomura & Tamaki PRD(05)ht [+ non-linear electromagnetism].
@ Discrete spectrum: Bekenstein & Mukhanov PLB(95)gq; Khriplovich PLB(98)gq [equidistant]; Hod GRG(99)gq/00; Bekenstein in(02)ht/01; Barvinsky et al FP(02) [charged black holes]; Das et al MPLA(02)ht, PLB(03)ht/02 [equivalence of approaches]; Polychronakos PRD(04)ht/03 [equidistant]; Oppenheim PRD(04)gq/03 [and quasi-normal modes]; Gour & Suneeta CQG(04)gq [different spectra]; Bekenstein PRD(15)-a1505 [Kerr black hole]; Hod EPJC-a1505 [the effective zero-point quantum-gravity fluctuation temperature agrees with the Hawking temperature].
@ Quantum-gravity effects, corrections, 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(09)-a0812 [phase transition and no radiation near Planck scale]; Nicolini & Rinaldi PLB(11)-a0910 [and minimal length]; Takahashi & Soda CQG(10)-a1004; Banerjee et al PRD(10)-a1005 [correction to TH]; Barbado et al JHEP(11) [the trans-Planckian problem as a guiding principle]; Yoon JKPS(16)-a1210; Corda EJTP-a1212 [problem for loop quantum gravity?].
@ 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 & Stojković PRD(09)-a0812 [unparticles]; Nowakowski & Arraut MPLA(09)-a0905 [minimum and maximum temperature]; Braunstein & Patra PRL(11)-a1102 + news pw(11)aug [derivation without spacetime]; Kawai et al a1203-wd [spacetime structure]; Oda a1503 [radiation inside black holes].
@ Other approaches: Bekenstein & Gour PRD(02)gq [eff]; Dolan JHEP(05)ht/04 [event horizon as fuzzy sphere].

Specific Types of Black Holes
@ Schwarzschild: Kastrup ht/98 [higher-dimensional]; Oliveira-Neto PRD(98) [Schwarzschild-de Sitter]; Böhmer & Vandersloot PRD(07)-a0709 [lqg, interior and singularity].
@ Kerr: Setare & Vagenas MPLA(05)ht/04; Vagenas JHEP(08)-a0804 [and quasinormal modes]; Medved CQG(08) [area spectrum].
@ Kerr-Newman: Mäkelä et al PRD(01); Gour & Medved CQG(03).
@ Reissner-Nordström: Kenmoku et al PRD(99)gq/98 [Reissner-Nordström-de Sitter]; Setare PRD(04)ht/03 [extremal, and quasinormal modes]; Dappiaggi & Raschi IJMPD(06)gq/05 [AdS-RN]; Oda a1503.
@ Other types: Peleg PLB(95) [dust]; Kowalski-Glikman PLA(98)gq [asymptotically-AdS]; Torres PLB(13)-a1309 [interior with inner horizon].

Evaporating Black Holes > s.a. black-hole radiation; non-commutative gravity; non-locality in quantum gravity.
* Remark: The results from semiclassical gravity are indicative of an important feature of full quantum gravity, and of a deep connection between quantum field theory, quantum gravity and thermodynamics, not yet understood; 1990, In particular, it is not clear whether a horizon will form in full quantum gravity as in the semiclassical theory, and where the radiation comes from physically.
* Spectrum: A line spectrum arises from transition between states, whose envelope is a (truncated) thermal spectrum; Line width ΔE ~ τ–1 ~ 1/30 of the line spacing; The spectrum is truncated because quanta that spend a long time near the horizon feel its quantum fluctuations.
* Radiation and cutoffs: Radiation seems not to be present if one puts a "hard" length cutoff, but survives a "soft" one.
* Corrections to radiation: Evaporation stops when the horizon radius reaches a scale at which spacetime becomes effectively 3-dimensional.
@ Reviews: Bekenstein in(99)gq/97, in(00)gq/98.
@ General references: Oda gq/97; Farley & D'Eath gq/05, gq/05 [late time evaporation], CQG(05), gq/05 + gq/05, AP(06)-a0708 [spin-1 and -2], CQG(05)gq [spin-1/2 amplitudes], GRG(06)gq/05 [Vaidya spacetime], PLB(06)gq, CQG(07)-a0708 [in terms of coherent and squeezed states]; Bonanno & Reuter PRD(06)ht [spacetime structure of evaporating black hole]; Nomura et al PRD(13)-a1210 [complete description of the formation and evaporation of a black hole].
@ And lqg: Modesto gq/06; Alesci & Modesto a1101; Barrau et al PRL(11)-a1109 + news tr(12)jan [quantum gravity (lqg) footprints]; Barman et al a1707 [the Hawking effect is short-lived in polymer quantization].
@ Related topics: Arzano MPLA(06), PLB(06)gq/05 [corrections in tunneling framework]; Hod & Keshet PRD(06) [selection rules]; Carlip & Grumiller PRD(11)-a1108 [and varying spacetime spectral dimension].

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