Maxwell's equal area law and the Hawking-Page phase transition
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.
Keywords
Cite
@article{arxiv.1310.2186,
title = {Maxwell's equal area law and the Hawking-Page phase transition},
author = {Euro Spallucci and Anais Smailagic},
journal= {arXiv preprint arXiv:1310.2186},
year = {2013}
}
Comments
15 pages, 4 Figures. Accepted for publication in Journal of Gravity