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: Compère gq/06-ln.

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

κ = 4π (r+c2GM)/A,      A = 4π Gc−4[2GM2Q2 + 2 (G2M4J2c2GM 2Q2)1/2] .

(While the other laws are analogous to the corresponding ones of ordinary thermodynamics, this law is not really analogous to the zeroth law.)

First Law > s.a. isolated horizons; Smarr Formula.
* Idea: The relationship usually called the "first law of black-hole thermodynamics" is actually the black-hole version of the fundamental identity of thermodynamics, analogous to dE = −p dV + T dS (rather than the first law dE = δW + δQ, which is a more general expression of the conservation of energy),

dM = Ω · dJ + (κ/4π) dA + Φ dQ ,

with Ω:= a/α = L/4M3 appearing in the expression for the Killing vector field tangent to the black-hole horizon la = ka + Ω ma (k and m are the timelike and spacelike Killing vectors, respectively), Ω = 4πJ/MA is constant for a stationary black hole, and Φ = 4π Qr+/A, where Q is here the black hole electric charge.
* Other backgrounds: It has been shown to hold in AdS black holes, but the correct results are from around 2005.
@ General references: Wald in(93)gq; 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]; Amsel et al PRD(08)-a0708 [physical process version, bifurcate Killing horizons]; Wall JHEP(09)-a0901 [critique of attempts at proof]; Ropotenko a1105; Dolan CQG(11)-a1106 [pressure and volume]; Corda JHEP(11)-a1107 [effective temperature and corrections]; Dolan in(12)-a1209 [pdV term]; Kelly JHEP(14)-a1408 [without entanglement]; Ma & Zhao CQG(14)-a1411 [corrected form]; Armas et al JHEP(16)-a1512 [gravitational tension and black-hole volume]; Rossi a2012-essay.
@ Quasilocal first law: Mukohyama & Hayward CQG(00)gq/99; Frodden et al PRD(13)-a1110; Chatterjee & Ghosh EPJC(18)-a1511 [from local Lorentz transformations].
@ Special types of black holes: Gao & Wald PRD(01)gq [charged, rotating]; Le Tiec et al PRD(12)-a1111, Blanchet et al PRD(13)-a1211 [binary black holes]; McCormick ATMP(14)-a1302 [Einstein-Yang-Mills black holes]; Johnstone et al PRD(13)-a1305 [extremal black holes]; Viaggiu GRG(15)-a1506 [for dynamical apparent horizons, black holes in FLRW universes]; Prabhu CQG(17)-a1511 [matter fields with internal gauge freedom]; > s.a. kerr spacetime; specific black-hole types.
@ 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; Chatterjee & Ghosh PRD(09)-a0812.
@ Black rings: Copsey & Horowitz PRD(06)ht/05 [dipole charges]; Astefanesei & Radu PRD(06)ht/05 [quasilocal]; Rogatko PRD(05)ht.
@ With matter: Rogatko PRD(98)ht [Einstein-Maxwell-axion-dilaton]; Gao PRD(03) [Einstein-Maxwell and Einstein-Yang-Mills]; Elgood et al a2006 [Einstein-Maxwell theory].
@ Modified gravity: Sermutlu CQG(98) [strings]; 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 NPB(08)-a0711 [including braneworld]; Miao et al JCAP(11)-a1107 [violation in f(T) gravity]; Kunduri & Lucietti CQG(14)-a1310 [5D]; Fan & Lü PRD(15)-a1501 [quadratically extended theories]; Arderucio-Costa a1905 [generic semiclassical theory]; > s.a. Smarr Formula.

(Generalized) Second Law (Area law) > s.a. black-hole entropy; entropy bounds; horizons; Penrose Process; specific black-hole types.
* Idea: For any process, dA > 0 (conjecture by Floyd and Penrose, proved by Christodoulou 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.
@ General references: 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]; 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 JHEP(07)-a0712 [dynamical horizons]; Kabe a1003/PRD; Chakraborty et al EPL(10)-a1009 [and nature of the entropy function]; Hod PLB-a1511 [and the hoop conjecture]; Cabero et al PRD(18)-a1711 [observational tests].
@ Modified versions: Davies & Davis FP(02) [cosmological]; Bernamonti et al JHEP(18)-a1803 [holographic]; Azuma & Kato a2001 [in terms of quantum conditional entropy].
@ 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]; Park IJMPA(09).
@ In other theories: Sadjadi PRD(07)-a0709 [f(R) gravity]; Akbar IJTP(09)-a0808 [Gauss-Bonnet and Lovelock gravity]; Sadjadi PS(11)-a1009 [Gauss-Bonnet gravity]; Sarkar & Wall PRD(11)-a1011 [Lovelock gravity, violation in black-hole merger]; Capela & Tinyakov JHEP(10)-a1102 [massive gravity]; Abdolmaleki et al PRD(14)-a1401 [scalar-tensor gravity]; Wall IJMPD(15)-a1504-GRF [higher-curvature gravity].
@ Possible violations: Shimomura et al PRD(00)gq/99; Park CQG(08)-ht/06; Eling & Bekenstein PRD(09)-a0810 [mechanisms that make it work]; Hu et al PRD(19)-a1906 [refutation of claim].

Third Law > s.a. specific black-hole types.
* Idea: There cannot be an equilibrium black hole with vanishing κ; 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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