On Thermodynamics of AdS Black Holes in Arbitrary Dimensions

Considering the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume as proposed in [1], we discuss the critical behavior of charged AdS black hole in arbitrary dimensions d. In particular, we present a comparative study in terms of the spacetime dimension d and the displacement of critical points controlling the transition between the small and the large black holes. Such behaviors vary nicely in terms of d. Among our result in this context consists in showing that the equation of state for a charged RN-AdS black hole predicts an universal number given by 2d-5 4d-8 . The three dimensional solution is also discussed.

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