Thermodynamics of Kerr-AdS black holes in the restricted phase space

Abstract

The thermodynamics for Kerr-AdS black hole in four dimensions is revisited using the recently proposed restricted phase space formalism, which includes the central charge $C$ of the dual CFT and the chemical potential $\mu$, but excludes the pressure and the conjugate volume, as thermodynamic variables. The Euler relation holds automatically, and the first order homogeneity of the mass and the zeroth order homogeneity of the intensive variables are made explicit. Thermodynamic processes involving each pair of conjugate variables are studied in some detail, with emphasis on the scaling properties of the equations of states. It turns out that the thermodynamic behavior of the Kerr-AdS black hole is very similar to that of the RN-AdS black hole studied earlier. In particular, it is found that, there is a first order supercritical phase equilibrium in the $T-S$ processes at fixed nonvanishing angular momentum, while at vanishing angular momentum or at fixed angular velocities, there is always a non-equilibrium transition from a small unstable black hole state to a large stable black hole state. Moreover, there is a Hawking-Page phase transition in the $\mu -C$ processes. Due to the complicatedness of the Kerr metric, the exact critical point and the Hawking-Page temperature are worked out explicitly only in the slow rotating limit, however the characteristic thermodynamic properties do not rely on the slow rotating approximation.

19 pages, 8 figures

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• Phase transition and Thermodynamical geometry of Reissner-Nordström-AdS Black Holes in Extended Phase Space
• Critical phenomena of static charged AdS black holes in conformal gravity
• Restricted phase space thermodynamics for AdS black holes via holography
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• Reentrant phase transitions and triple points of topological AdS black holes in Born-Infeld-massive gravity
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• Thermodynamics for higher dimensional rotating black holes with variable Newton constant
• Exploring the Phase Transition in Charged Gauss-Bonnet Black Holes: A Holographic Thermodynamics Perspectives
• Restricted phase space thermodynamics for black holes in higher dimensions and higher curvature gravities
• Black holes thermodynamics with CFT re-scaling
• Topology of the charged AdS black hole in restricted phase space
• Holographic Thermodynamics of BTZ Black Holes and Tsallis Entropy