Black Holes and Thermodynamics: The First Half Century

Grumiller, Daniel; McNees, Robert; Salzer, Jakob

doi:10.1007/978-3-319-10852-0_2

Cited by 13 publications

(15 citation statements)

References 334 publications

(411 reference statements)

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“…The thermodynamic variables in (2.6) are related by a useful Smarr-Gibbs-Duhem relation, which (in four dimensions) reads 4 M = 2(T S + ΩJ) + ΦQ , (2.8) expressing a relationship between the extensive (M, J, Q) and intensive (T, Ω, Φ) thermodynamic variables. For references on standard black hole thermodynamics, a variety of reviews are available [33][34][35][36].…”

Section: A Brief Review Of Standard Black Hole Thermodynamicsmentioning

confidence: 99%

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Black hole chemistry: thermodynamics with Lambda

Kubizňák

Mann

Teo

2017

Class. Quantum Grav.

757

657

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We review recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. In this approach, the mass of the black hole is no longer regarded as internal energy, rather it is identified with the chemical enthalpy. This leads to an extended dictionary for black hole thermodynamic quantities, in particular a notion of thermodynamic volume emerges for a given black hole spacetime. This volume is conjectured to satisfy the reverse isoperimetric inequalityan inequality imposing a bound on the amount of entropy black hole can carry for a fixed thermodynamic volume. New thermodynamic phase transitions naturally emerge from these identifications. Namely, we show that black holes can be understood from the viewpoint of chemistry, in terms of concepts such as Van der Waals fluids, reentrant phase transitions, and triple points. We also review the recent attempts at extending the AdS/CFT dictionary in this setting, discuss the connections with horizon thermodynamics, applications to Lifshitz spacetimes, and outline possible future directions in this field.

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Section: A Brief Review Of Standard Black Hole Thermodynamicsmentioning

confidence: 99%

“…where the "thermodynamic volume" is now 35) and the area A Σ was found by imposing a cutoff [232]. Using (5.30) and (5.1), the extended bulk first law can be rewritten as…”

Section: Holographic Entanglement Entropymentioning

confidence: 99%

Black hole chemistry: thermodynamics with Lambda

Kubizňák

Mann

Teo

2017

Class. Quantum Grav.

757

657

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“…The discovery of a rational basis for assigning entropy to black holes and the formulation of a generalized second law that includes black hole interactions have spawned a huge amount of research that would take us too far afield to discuss here. See the companion article by Jacobson [48] and also [49] for reviews and references. Perhaps the most interesting question that has come out of this is what the entropy of a black hole represents microscopically.…”

Section: The Quantum Eramentioning

confidence: 99%

The Kerr metric

Teukolsky

2015

Class. Quantum Grav.

160

131

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Abstract. This review describes the events leading up to the discovery of the Kerr metric in 1963 and the enormous impact the discovery has had in the subsequent 50 years. The review discusses the Penrose process, the four laws of black hole mechanics, uniqueness of the solution, and the no-hair theorems. It also includes Kerr perturbation theory and its application to black hole stability and quasi-normal modes. The Kerr metric's importance in the astrophysics of quasars and accreting stellar-mass black hole systems is detailed. A theme of the review is the "miraculous" nature of the solution, both in describing in a simple analytic formula the most general rotating black hole, and in having unexpected mathematical properties that make many calculations tractable. Also included is a pedagogical derivation of the solution suitable for a first course in general relativity.

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“…For more background on the mathematics and physics of black holes, we refer the reader to [124]. We refer to [32,33] for reviews that focus on the particular role of conformal field theory in understanding quantum gravity.…”

Section: Question 1 Assuming That the Moonshine Module V Serves As Tmentioning

confidence: 99%

Moonshine

Duncan

Griffin

Ono

2015

Mathematical Sciences

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illustrate the case of J(τ ) = j(τ ) − 744, whose coefficients turn out to be sums of the dimensions of the 194 irreducible representations of M. Such formulas are dictated by the structure of the graded monstrous moonshine modules. Recent works in moonshine suggest deep relations between number theory and physics. Number theoretic Kloosterman sums have reappeared in quantum gravity, and mock modular forms have emerged as candidates for the computation of black hole degeneracies. This paper is a survey of past and present research on moonshine. We also compute the quantum dimensions of the monster orbifold and obtain exact formulas for the multiplicities of the irreducible components of the moonshine modules. These formulas imply that such multiplicities are asymptotically proportional to dimensions.

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Black Holes and Thermodynamics: The First Half Century

Cited by 13 publications

References 334 publications

Black hole chemistry: thermodynamics with Lambda

Black hole chemistry: thermodynamics with Lambda

The Kerr metric

Moonshine

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