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
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 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*. 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, i.e. P=P(V), in terms of the geometrical volume V=4\pi r^3/3.
\end{abstract}
