Black-Hole
Entropy| Black-Hole
Entropy |
In General > s.a. black-hole thermodynamics;
origin of black-hole entropy; specific
types of black holes.
* Idea: Black-hole entropy
was introduced in a formal way; Several interpretations of it have been proposed,
some of which are variations on Bekenstein's original
idea that it corresponds to the log of "distinct quantum internal
states" of the black hole, S = kB ln
W, but in general it is not clear what this W means physically;
Classically, one has to use S = 
to
avoid inconsistencies with the second law, but quantum mechanically there is
black-hole radiation and all is ok.
* Schwarzschild: A Schwarzschild
black hole of classical surface area AH has
entropy (in any dimension)
SB = 
(kBc3/G
) AH .
* Reissner-Nordström:
An extremal black hole has S = 0 but A 
0.
* Remark: With matter
fields, in general S A/4;
It is possible to form
black holes without a global increase in entropy.
* Orders of magnitude: Compare SSun =
1058 with
Ssolar mass bh = 1077.
@ Reviews: Mitra ht/96;
Frolov & Fursaev CQG(98)ht;
Majumdar gq/98-in, ht/01-in;
Mukohyama gq/99-in;
Damour ht/04-in;
Jacobson et al IJTP(05)ht-in
[trialogue on interpretation]; Soloviev gq/05-in;
Mitra a0902-in.
@ General references: Wald PRD(79);
Gould PRD(87);
Martinez & York PRD(89);
Hiscock PRD(89);
Frolov & Novikov PRD(93)gq;
Wald PRD(93)gq [Noether
charge]; Dowker CQG(94);
Teitelboim ht/94 [and
dimensional continuation];
Frolov ht/94-in,
ht/95-in;
Jacobson et al PRD(94)gq/93;
Brown & York gq/94-in
[path integral]; Martinez PRD(95)gq/94 [microcanonical];
Brown PRD(95)gq [from
Hamiltonian]; Pretorius
et al PRD(98)gq/97 [operational];
Kay ht/98;
Mäkelä & Repo gq/98;
Medved gq/04 [re
interpretation]; Sorkin SHPMP(05)ht-in
[point of view]; Cadoni MPLA(06)ht/05;
Jacobson et al IJTP(05)
[views]; Carlip JPCS(07)gq,
GRG(07)-a0705-GRF,
a0807-in [the
problem of universality].
@ Properties: Iyer & Wald PRD(94)gq,
PRD(95)gq;
Lau gq/94;
Bekenstein gq/94-in;
Solodukhin PRD(96)
[approaches agree]; Corichi & Sudarsky MPLA(02)gq/00 [and
area];
Major & Setter CQG(01)
[universality]; Åman
et al GRG(03)gq [and
state space metric]; Saida PTP-a0910 [and area, violation of relationship].
@ Related topics: Lue & Weinberg GRG(00)gq [and
monopoles]; Borsten et al PRP(09) [in string theory, and entanglement of qubits
and qutrits]; > s.a. gravitational
phenomenology [spacetime
measurement].
Corrections > s.a. 2D gravity;
3D black holes; 3D quantum
gravity; black-hole radiation; quantum
black holes; specific types of black holes.
* Reasons: Can be due
to thermal fluctuations around an equilibrium canonical ensemble, or quantum
spacetime fluctuations within a microcanonical
framework;
Typically, higher-order gravity theories give corrections of the form AH R, R2,
etc, while various approaches to effective quantum gravity corrections give
terms of the form ln
AH.
@ From partition function: Gibbons & Hawking PRD(77); York PRD(86).
@ Quantum / log corrections: Susskind & Uglum PRD(94)
[canonical quantum gravity and string theory]; Mitra gq/95-in;
Ghosh & Mitra PRD(97);
Carlip CQG(00)gq [log,
Cardy formula];
Kaul & Majumdar PRL(00);
Das et al CQG(02)ht/01, ht/02-in;
Gour PRD(02)gq [log];
Mukherji & Pal JHEP(02)ht [AdS-cft];
Chatterjee & Majumdar gq/03, PRL(04)gq/03 [log,
non-rotating];
Akbar & Das CQG(04)ht/03 [Schwarzschild
and Reissner-Nordström, thermal]; Bhaduri et al PRD(04)gq/03 [microcanonical];
Ghosh & Mitra PRD(05)gq/04;
Hod CQG(04)ht [higher-order];
Medved CQG(03)
[2D], CQG(05)gq/04,
CQG(05)gq/04;
Medved & Vagenas PRD(04)ht [using
gup]; Zhao et al MPLA(07)gq/06;
Shankaranarayanan MPLA(08)-a0805;
Pankovic et al a0810.
@ Renormalized: Odintsov & Yoon IJMPA(96)gq/95;
Larsen & Wilczek NPB(96).
@ Higher-derivative gravity:
Correa-Borbonet BJP(05)ht-in
[Lovelock
theory]; Kraus & Larsen JHEP(05)ht.
@ Related topics: Belgiorno & Liberati GRG(97)gq/96 [and
Casimir effect]; Liberati NCB(97)gq/96 ["intrinsic" thermodynamics];
Strominger JHEP(98)ht/97 [anti-de Sitter
geometry]; Jacobson gq/99-in
[partial horizon]; Wu IJMPD(00)gq [topology];
Dreyer et al CQG(01)gq [symmetries];
Carlip PRL(02)gq [conformal
symmetry]; More CQG(05)gq/04 [higher-order
corrections]; > s.a. entropy.
Other Related Topics > see thermodynamical systems [contribution to cosmological entropy]; fine-structure constant [variation].
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14 oct 2009