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

Abstract EN

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 temperature T>T*, while pure radiation persists for 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 entropy S=A/4, one has to write a black hole equation of state, that is, P=PV, in terms of the geometrical volume V=4πrH3/3.