The first law of thermodynamics for Kerr–anti-de Sitter black holes

By G. W. Gibbons, M. Perry, C. Pope. 2004

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We obtain expressions for the mass and angular momenta of rotating black holes in anti-de Sitter backgrounds in four, five and higher dimensions. We verify explicitly that our expressions satisfy the first law of thermodynamics, thus allowing an unambiguous identification of the entropy of these black holes with of the area. We find that the associated thermodynamic potential equals the background-subtracted Euclidean action multiplied by the temperature. Our expressions differ from many given in the literature. We find that in more than four dimensions, only our expressions satisfy the first law of thermodynamics. Moreover, in all dimensions we show that our expression for the mass coincides with that given by the conformal conserved charge introduced by Ashtekar, Magnon and Das. We indicate the relevance of these results to the AdS/CFT correspondence.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/478e6c08ef2e2d43c6191fa56d750ec37ee79dcf

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Citations in the corpus

Comments on string theory backgrounds with non-relativistic conformal symmetry (2008, methodology): “The P− and P+ can be calculated by starting from the expressions for the energy and the angular momentum in [29] (also see [30]) and taking the appropriate limit, see appendix B.”
Large rotating AdS black holes from fluid mechanics (2007, methodology): “7) of [16] is different form the sign given in equation (4.”
Thermodynamics of black holes in two (and higher) dimensions (2007, background): “For a discussion of alternative forms of this relation relevant for BHs, see [36].”
Action growth for AdS black holes (2016, methodology): “We use the conventions and results in [29] for the thermodynamics of Kerr-AdS black holes.”
Black rings in (Anti)-de Sitter space (2008, background): “Their mass, angular momenta, area and surface gravity, as computed in [21], are M = mΩd−2 4π ∏”
An instability of higher-dimensional rotating black holes (2010, background): “The mass M and angular momentum J , defined with respect to ∂ψ, are [10]”
Hawking radiation from AdS black holes (2009, methodology): “This was computed carefully in [50] with the result”
AdS and Lifshitz black holes in conformal and Einstein-Weyl gravities (2012, methodology): “8) coincide with those obtained from the AMD method and in particular, by setting α = 12 , we recover the result presented in [72] and [80], thus confirming the tree level equivalence between Einstein gravity and Weyl gravity that was proposed in [38].”
Black hole enthalpy and an entropy inequality for the thermodynamic volume (2010, methodology): “As discussed in [8], the various thermodynamic quantities are now given by”
Kerr-AdS/CFT correspondence in diverse dimensions (2008, unknown): “The thermodynamic quantities for the Kerr-AdS solutions were obtained in [19].”
Black hole chemistry: thermodynamics with Lambda (2016, unknown): “Similarly, Ω = Ω − Ω + ∞ i i i , where the quantities Ω∞ i allow for the possibility of a rotating frame at infinity [55].”
Thermodynamics of Rotating Black Holes and Black Rings: Phase Transitions and Thermodynamic Volume (2014, background): “The thermodynamic quantities associated with KerrAdS black holes were first calculated in [107].”
Black Hole Chemistry (2014, background): “rotation parameters, where the quantities Ω∞ allow for the possibility of a rotating frame at infinity [7, 8].”