Table of Contents
Journal of Gravity
Volume 2013 (2013), Article ID 525696, 7 pages
http://dx.doi.org/10.1155/2013/525696
Research Article

Maxwell’s Equal Area Law and the Hawking-Page Phase Transition

Dipartimento di Fisica Teorica, Università di Trieste and INFN, 34151 Sezione di Trieste, Italy

Received 24 June 2013; Revised 12 September 2013; Accepted 8 October 2013

Academic Editor: Jose Antonio De Freitas Pacheco

Copyright © 2013 Euro Spallucci and Anais Smailagic. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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   in the temperature-entropy plane, in order to eliminate negative heat capacity BHs. The construction we present here is reminiscent of the isobar cut in the pressure-volume plane which eliminates unphysical part of the Van der Walls curves below the critical temperature. Our construction also modifies the Hawking-Page phase transition. Stable BHs are formed at the temperature , while pure radiation persists for . turns out to be below the standard Hawking-Page temperature and there are no unstable BHs as in the usual scenario. Also, we show that, in order to reproduce the correct BH entropy , one has to write a black hole equation of state, that is, , in terms of the geometrical volume .