Maxwell's equal area law and the Hawking-Page phase transition

TL;DR

This paper applies Maxwell's equal area law to Schwarzschild-AdS black holes, modifying the Hawking-Page transition and providing a new equation of state to correctly reproduce black hole entropy.

Contribution

It introduces a Maxwell equal area construction in the temperature-entropy plane for black holes, refining the understanding of phase transitions in AdS black hole thermodynamics.

Findings

Eliminates negative heat capacity black holes via Maxwell construction.

Revises the Hawking-Page transition temperature to below the standard value.

Derives a black hole equation of state consistent with entropy S=A/4.

Abstract

In this paper we study the phases of a Schwarzschild black hole in the Anti deSitter background geometry. Exploiting fluid/gravity duality we construct the Maxwell equal area isotherm T=T* in the temperature-entropy plane, in order to eliminate negative heat capacity black hole configurations. The construction we present here is reminiscent of the isobar cut in the pressure-volume plane which eliminates un-physical part of the Van der Walls curves below the critical temperature. Our construction also modifies the Hawking-Page phase transition. Stable black holes are formed at the temperature T > T*, while pure radiation persists for T< T*. T* turns out to be below the standard Hawking-Page temperature and there are no unstable black holes as in the usual scenario. Also, we show that in order to reproduce the correct black hole entropy S=A/4, one has to write a black hole equation of state, i.e. P=P(V), in terms of the geometrical volume V=4\pi r^3/3.