On thermodynamics of AdS black holes in arbitrary dimensions

Considering the cosmological constant Λ as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume as proposed by Kubiznak and Mann [J. High Energy Phys. 1207 (2012) 033], 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. Our result shows that the equation of state for a charged Reissner - Nordstrom AdS black hole predicts an universal number given by (2d - 5)/(4d - 8). The three-dimensional solution is also discussed. © 2012 Chinese Physical Society and IOP Publishing Ltd.