Laws of Black Hole Thermodynamics  

In General > s.a. black hole thermodynamics and specific black hole types; gravitational thermodynamics.
* In various theories: Laws of black hole mechanics can be derived in any theory of gravity by varying the expression that gives their energy as a function of various parameters; If the theory is diffeomorphism-invariant, the entropy term will be proportional to the horizon area; The specific form of the field equations enters in the coefficient of dS in the first law – the expression for T – and in the greybody factors for the radiation spectrum (as Visser pointed out, the field equations are not directly involved in the fact that there is radiation); Similarly, obtaining the right form of the entropy or radiation spectrum in the semiclassical sector of a theory of quantum gravity only indicates that the limit is consistent with classical gravity.
@ Intros, reviews: Compere gq/06-ln.

Zeroth Law
* Idea: The surface gravity is constant on the horizon, like temperature; For a Kerr-Newman black hole,

= 4 (r+c2 – GM)/A,      A = 4Gc–4[2GM2 – Q2 + 2 (G2M4 – J2c2 – GM2Q2)1/2] .

First Law > s.a. horizons; kerr; Smarr Formula; specific black hole types.
* Idea: Conservation of energy, analogous to E = –p V+ T S,

M = · J + (/4) A +  Q ,

with := a/ = L/4M3 appearing in the expression for the Killing vectior field tangent to the black hole horizon la = ka + ma (k and m are the timelike and spacelike Killing vectors, respectively), = 4J/MA is constant for a stationary black hole, and = 4Qr+/A.
* Other backgrounds: Has been shown to hold in AdS black holes, but the correct results are from around 2005.
@ General references: Wald gq/93-in; Sorkin & Varadarajan CQG(96)gq/95; Iyer PRD(97)gq/96; Fursaev PRD(99)ht/98 [energy vs Hamiltonian]; Fatibene et al AP(99)ht/98; Hayward CQG(98)gq/97 [and relativistic thermodynamics]; Mukohyama PRD(99)gq/98 [Noether charge form], & Hayward CQG(00)gq/99 [quasilocal]; Gao & Wald PRD(01)gq [charged, rotating]; Amsel et al a0708 [physical process version, bifurcate Killing horizons].
@ Isolated, dynamical horizons: Ashtekar et al PRD(00)gq, PRD(01)gq [rotating]; Allemandi et al gq/01; Booth & Fairhurst PRL(04)gq/03; Hayward PRD(04)gq.
@ Black rings: Copsey & Horowitz PRD(06)ht/05 [dipole charges]; Astefanesei & Radu PRD(06)ht/05 [quasilocal]; Rogatko PRD(05)ht.
@ Modified theories: Rogatko PRD(98)ht [Einstein-Maxwell-axion-dilaton]; Sermutlu CQG(98) [strings]; Gao PRD(03) [Einstein-Maxwell and Einstein-Yang-Mills]; Koga PRD(05)ht [higher-order, AdS black holes]; Kastor & Traschen JHEP(06) [Kaluza-Klein black holes]; Rogatko PRD(07)-a0705 [for black saturns]; Wu et al a0711-NPB [including braneworld]; > s.a. Smarr Formula.

Second Law (Area law) > s.a. black hole entropy; entropy bounds; horizons; Penrose Process.
* Idea: For any process, dA > 0 (conjecture by Floyd and Penrose, proved by DC for some processes, and as a general theorem by Hawking, assuming the weak energy condition holds), which influences the amount of energy we can extract from a black hole, A black hole entropy; The proof of this has been reduced to the cosmic censorship conjecture.
@ Generalized: Bekenstein PRD(73), PRD(74); Hawking PRD(76); Unruh & Wald PRD(82); Sewell PLA(87); Frolov & Page PRL(93)gq [quasistationary]; Mukohyama PRD(97)gq/96 [non-eternal]; Sung gq/97; Bekenstein PRD(99)gq [quantum buoyancy]; Shimomura & Mukohyama PRD(00)gq/99 [charged particles]; Gao & Wald PRD(01)gq [charged, rotating]; Davies & Davis FP(02) [cosmological]; Davis et al CQG(03)ap; Matsas & Rocha da Silva PRD(05)gq [thought experiment]; Saida CQG(06)gq [and radiation as non-equilibrium process]; He & Zhang a0712-JHEP [dynamical horizons].
@ And entropy bounds: Pelath & Wald PRD(99)gq; Flanagan et al PRD(00)gq/99.
@ Related topics: Giulini JMP(98)gq [cusps on horizon]; Song & Winstanley IJTP(08)gq/00 [and information theory].
@ In other theories: Sadjadi PRD(07)-a0709 [f(R) gravity].
@ Possible violations: Shimomura et al PRD(00)gq/99; Park ht/06.

Third Law > s.a. specific black hole types.
* Idea: There cannot be an equilibrium black hole with vanishing ; Like T in the third law of thermodynamics.
* Remark: The Nernst formulation does not apply to rotating black holes.
@ References: Carter in(79); Israel PRL(86); Roman GRG(88); Dadhich & Narayan PLA(97)gq [and gravitational charge]; Wald PRD(97)gq; Rácz CQG(00)gq; Lowe PRL(01)gq/00 [semiclassical]; Liberati et al IJMPD(01)gq/00 [extremal].

Related Topics
@ Fourth law: Loustó NPB(93)gq [scaling laws in critical transitions].

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