Origin of Black-Hole Entropy| Origin of Black-Hole Entropy |
Proposals Based on Black-Hole Microstates
> s.a. black-hole entropy [reviews].
@ Fluctuations: Gerlach PRD(76);
York PRD(83),
in(84);
Pavón & Rubí PRD(88);
Frolov PRL(95);
Sorkin & Sudarsky CQG(99)gq;
Gour & Medved CQG(03)gq;
Requardt a0708.
@ Spacetime microstructure: Scardigli CQG(97)gq [foam];
Padmanabhan PRL(98)ht;
Garattini Ent(00)gq [foam, Schwarzschild-de Sitter space],
IJMPD(02)gq/00;
Bergamin & Grumiller IJMPD(06)gq-GRF;
Tanaka EPJP(14)-a1304 [non-commutative spacetime];
Davidson a1907 [horizon tiling configurations].
@ Horizon microstates: Sfetsos & Skenderis NPB(98)ht/97;
Brown PRD(98);
Epp & Mann MPLA(98)gq,
Epp gq/98/PRD [tetrad approach];
Cvetič & Larsen PRL(99) [rotating];
Soloviev PRD(00)ht/99;
Dou & Sorkin FP(03)gq,
Rideout & Zohren in(08)gq/06 [causal links];
Das & Shankaranarayanan CQG(07)gq;
Silva & Landim EPL(11)-a1003 [based on fuzzy space];
Ghosh IJTP(11)-a1008 [Shannon entropy];
Chung NPB(12).
@ Horizon conformal field theory:
Carlip gq/95,
gq/96-conf,
PRD(97)gq/96 [3D],
NPPS(97)gq,
PRL(99)ht/98,
CQG(99)gq,
NPPS(00)gq/99;
Park NPB(02)ht/01 [deformations];
Carlip CQG(05)ht/04 [stretched horizon],
CQG(05)gq-in,
IJTP(07)gq/06-conf [horizon constraints and symmetry algebra];
Carlip AIP(12)-a1207 [rev].
@ Loop quantum gravity:
Garay & Mena CQG(03),
Ghosh & Mitra PLB(05)gq/04 [and Immirzi parameter];
Domagała & Lewandowski CQG(04)gq;
Meissner CQG(04)gq;
Swain IJMPD(05)gq-GRF;
Mitra a0705-conf [state counting];
Tamaki CQG(07)-a0707;
Jacobson CQG(07)-a0708 [and renormalization];
Sahlmann PRD(07)-a0709;
Barbero & Villaseñor CQG(09)-a0810;
Agulló et al JCAP(09)-a0903 [conformal-field-theory perspective],
PRD(09)-a0906;
Bianchi CQG(11)-a1011 [and polymer physics];
Cao & Barrau a1111 [for large black holes];
Dasgupta Sigma(13)-a1203 [and semiclassical states];
Bianchi a1204 [non-extremal black holes];
Livine & Terno CQG(12)-a1205;
Ghosh & Perez a1210 [scaling];
Ghosh et al PRD(14)-a1309 [statistics and holography];
Frodden et al EPL(14)-a1312 [complex variables];
Bodendorfer CQG(14)-a1402 [and entanglement entropy];
Han a1402;
Pigozzo et al CQG(20)-a2001 [and Immirzi parameter].
@ Spin-foam quantum gravity: García-Islas CQG(08)-a0809;
García-Islas CQG(10)-a1004 [statistical calculation].
@ Strings, M-theory: Horowitz & Strominger PRL(96) [near extremal];
Strominger & Vafa PLB(96);
Horowitz & Marolf PRD(97)ht/96;
Maldacena et al JHEP(97)ht,
Horowitz & Roberts PRL(07) [extremal, in M-theory];
Lowe PRL(98);
Dabholkar IJMPD(06).
> Related topics: see 2D
and 3D black holes; 2D gravity;
quantum black holes; spin-foam models.
Other Origin and Approaches > s.a. gravitational thermodynamics;
horizons; non-extensive statistical mechanics.
* Ways of forming the black hole:
S is the log of the number of quantum mechanically distinct ways that
the black hole could have been made, or information lost in the creation of the
black hole; This leads to an estimate of the quantum black hole level spacing.
* Entanglement entropy:
Black-hole entropy is semi-classical, in the sense that it comes from tracing
out over internal degrees of freedom of quantum fields in a classical geometry,
without even backreaction – related to the "brick wall model"
idea; It appears to be proportional to A for fields in the ground
state or in coherent/squeezed states, not in excited states.
* Species problem: The fact that
the Bekenstein-Hawking entropy is independent of the number of particle species,
while entanglement entropy gives a contribution that appears to depend on the
number of species.
@ Ways of forming the black hole: & Bekenstein; & Hawking;
Zurek & Thorne PRL(85);
Mukhanov FP(03);
Hsu & Reeb PLB(08)-a0706 [and monster states];
Zhang et al GRG(11)-a1102.
@ Entanglement entropy: Sorkin in(83);
Bombelli et al PRD(86);
Srednicki PRL(93);
Jacobson gq/94 [and induced gravity];
Kabat NPB(95)ht [and 1-loop corrections];
Muller & Loustó PRD(95);
Ahmadi et al CJP(06)ht/05-in [deviations from area law];
Ansari NPB(08)gq/06 [in lqg];
Emparan JHEP(06) [holographic derivation];
Das & Shankaranarayanan JPCS(07)gq/06,
Das et al PRD(08)-a0705,
CJP(08)-a0708-conf [power-law corrections in different states];
Das et al a0806-ch [rev];
Braunstein et al PRL(13)-a0907 [and information retrieval];
Arenas & Tejeiro NCB(10)-a1108;
Solodukhin LRR(11);
Giaccari et al EPJC(18)-a1512 [finite];
Garfinkle a1901 [as a consequence of excision].
@ Species problem: Brout IJMPD(09)-a0802;
Dvali & Solodukhin a0808;
Chen et al EPJC(18)-a1609,
Rojas & Arenas a1712 [proposed solutions].
@ And brick wall: Mukohyama et al PRD(97)gq;
Mukohyama PhD(98)gq,
gq/99-conf;
Jing & Yan PRD(99)gq [Kerr];
Garattini MPLA(04) [and spacetime foam].
@ Contributions from other fields: Donnelly & Wall PRD(12)-a1206 [gauge-field contribution].
@ Other proposals:
Yang MPLA(01) [topological invariants];
Badiali JPA(06)gq/05 [spacetime order];
Banerjee et al a0804 [horizon chiral Virasoro algebra];
Hadad & Kupferman a1006-wd [Wald and statistical entropies];
Nicolini & Singleton PLB(14)-a1409 [as the statistical entropy of a gas of voxels];
Kalogeropoulos a1711,
IJGMP(18)-a1712 [mesoscopic treatment, from horizon topology];
Xiao PRD(20)-a1910 [microscopic derivation];
Roy Chowdhury et al a2103 [from the Einstein boundary term].
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