On Thermodynamics of AdS Black Holes in Arbitrary Dimensions

TL;DR

This paper explores the thermodynamic behavior of charged AdS black holes across various dimensions, revealing how critical points and phase transitions depend on spacetime dimensionality and identifying a universal ratio for the equation of state.

Contribution

It provides a comparative analysis of critical phenomena in charged AdS black holes across arbitrary dimensions, including a universal ratio for the equation of state.

Findings

Critical behavior varies with spacetime dimension d.

Universal ratio for the equation of state: (2d-5)/(4d-8).

Three-dimensional case discussed.

Abstract

Considering the cosmological constant $\Lambda$ as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume as proposed in Kubiznak and Mann (2012), 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 $\frac{2d-5}{4d-8}$. The three dimensional solution is also discussed.