Quantum
Black-Hole Radiation / Spectrum| 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 no, of degeneracy 
=
2 n–1 (from S 
ln and S = A/4),
so M n1/2;
Lifetime of a level 
3840 
–1 M ln2, 1;
(Hod) A = 4n
/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-in;
Kunstatter PRL(03)gq/02;
Abdalla et al MPLA(03)gq [quasi-extremal];
Gegenberg et al CQG(06)gq [midi-superspace
approach].
@ 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-in;
Krasnov CQG(99)gq/97;
Berezin et al PLB(99)gq/98,
G&C(99);
Berezin IJMPA(02)gq/01-in;
Khriplovich
gq/04-in
[and correspondence], IJMPD(05)
[and quasinormal modes]; Das et al CQG(05)ht/04 [rotating,
any dimension]; Setare ht/05-in;
Ansari NPB(07)ht/06,
Díaz-Polo & Fernández-Borja CQG(08)-a0706 [lqg];
Parwani a0904-in
[corrections to equispaced spectrum]; Medved a0906,
Ropotenko PRD(09) [equal spacing].
@ 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: 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].
@ Other approaches: Bekenstein & Gour PRD(02)gq [eff];
Dolan JHEP(05)ht/04 [event
horizon as fuzzy sphere].
@ 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].
@ Other types: Peleg PLB(95)
[dust]; Oda gq/97 [evaporating];
Kowalski-Glikman PLA(98)gq [asymptotically-AdS].
Evaporating Black Holes > s.a. black-hole
radiation.
* 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 
E –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.
* Rad and cutoffs: Radiation
seems not to be present if one puts a "hard" length
cutoff, but survives a "soft" one.
@ Reviews: Bekenstein in(99)gq/97,
in(00)gq/98.
@ General references: 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], gq/06,
CQG(07)-a0708 [in
terms of
coherent and squeezed states]; Arzano MPLA(06), PLB(06)gq/05 [corrections
in tunneling framework]; Hod & Keshet PRD(06)
[selection rules]; Bonanno & Reuter PRD(06)ht [spacetime
structure of evaporating black hole]; Modesto gq/06 [lqg].
main page – abbreviations – journals – comments – other
sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified
31 aug 2009