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].
@ 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).
@ 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].
@ 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).
@ 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.
@ Spin-foam quantum gravity: García-Islas CQG(08)-a0809; García-Islas CQG(10)-a1004 [statistical calculation].
> 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: Zurek & Thorne PRL(85); & Bekenstein; & Hawking; 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).
@ Species problem: Brout IJMPD(09)-a0802; Dvali & Solodukhin a0808; Chen et al a1609 [proposed solution].
@ 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].


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