Enthalpy and the mechanics of AdS black holes
By David Kastor, Sourya Ray, Jennie Traschen. 2009
1,497 citations recorded by the source corpus.
We present geometric derivations of the Smarr formula for static AdS black holes and an expanded first law that includes variations in the cosmological constant. These two results are further related by a scaling argument based on Euler's theorem. The key new ingredient in the constructions is a two-form potential for the static Killing field. Surface integrals of the Killing potential determine the coefficient of the variation of Λ in the first law. This coefficient is proportional to a finite, effective volume for the region outside the AdS black hole horizon, which can also be interpreted as minus the volume excluded from a spatial slice by the black hole horizon. This effective volume also contributes to the Smarr formula. Since Λ is naturally thought of as a pressure, the new term in the first law has the form of effective volume times change in pressure that arises in the variation of the enthalpy in classical thermodynamics. This and related arguments suggest that the mass of an AdS black hole should be interpreted as the enthalpy of the spacetime.
Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/ea1d7319c44b90d83a18eaea47d263134b5efb39
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Citations in the corpus
- Reentrant phase transitions in rotating anti–de Sitter black holes (2013, background): “We interpret the negative cosmological constant Λ as a positive thermodynamic pressure P [7, 10, 18, 19]”
- Construction of Regular Black Holes in General Relativity (2016, neutral): “For the electrically charged case (38), the solution reads ds(2) = −fdt(2) + dr 2 f + r(2)dΩ(2)k , f = r (2)/`(2) + k − 2M r − 2α −1q3rμ−1 ( rν + qν )μ/ν , A = q √ 2α (( 3− (μ− 3)( qr ) ν )( 1 + ( qr ) ν )−μ+ν ν − 3 ) dt , (54) Treating the cosmological constant as well as the parameter α as a therm”
- Holographic heat engines (2014, background): “[9] proposed that the extension shifts the identification of the mass M from being the energy U to being the enthalpy, to wit: M = H ≡ U + pV , so the First Law now becomes:”
- Ruppeiner geometry, phase transitions, and the microstructure of charged AdS black holes (2019, background): “Scaling relations imply that the Smarr formula relating the various thermodynamic parameters of a black hole only holds when the variation of the cosmological constant is included [37].”
- Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space (2020, background): “with the interpretation that the cosmological constant is the pressure [1]”
- Thermodynamic Volumes and Isoperimetric Inequalities for de Sitter Black Holes (2013, methodology): “[3] D.”
- Topology of black hole thermodynamics (2021, background): “D 60, 064018 (1999), [arXiv:hep-th/9902170 [hep-th]] [9] D.”
- Effects of dark energy on P–V criticality of charged AdS black holes (2014, background): “Treating the cosmological constant as thermodynamic pressure, black hole thermodynamics in the extended phase space has gained more and more attention recently [3]- [29] and the analogy between charged AdS black holes and liquid-gas systems has been further enhanced.”
- On the critical phenomena and thermodynamics of charged topological dilaton AdS black holes (2013, background): “Motivated by the AdS/CFT correspondence[11], where the transitions have been related with the holographic superconductivity[12, 13], the subject that the phase transitions of black holes in asymptotically anti de-Sitter (AdS) spacetime, has received considerable attention[14, 15, 16, 17, 18].”
- Black Hole Chemistry (2014, background): “This rather novel idea originates from a consideration of th e Smarr relation[2, 3].”
- Smarr formula and an extended first law for Lovelock gravity (2010, methodology): “The contribution to the first law from a varying cosmological constant was computed and used to obtain the Smarr formula in [35].”