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

摘要

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 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 temperatureT>T*, while pure radiation persists forT<T*.T*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 entropyS=A/4, one has to write a black hole equation of state, that is,P=PV, in terms of the geometrical volumeV=4πrH3/3.