Maxwell's equal area law for charged Anti-deSitter black holes

TL;DR

This paper applies Maxwell's equal area law to charged Anti-deSitter black holes, providing exact solutions for isotherms and entropies, and linking extremal black holes to stable molecules in Van der Waals fluids.

Contribution

It introduces an exact isothermal construction for charged AdS black holes and explores the thermodynamic duality with Van der Waals fluids.

Findings

Exact solutions for isotherms and entropies of black holes.

Removal of unphysical negative heat capacity regions.

Extremal black holes correspond to stable, un-shrinkable molecules.

Abstract

In this paper we present the construction of the Maxwell equal area law in the Hawking temperature graph for a charged black hole in Anti-deSitter background. We are able to find exact solution for the corresponding isotherm and entropies for "gaseous" (large) black holes and "liquid" (near-extremal) black holes. Isothermal construction removes the unphysical, negative heat capacity, regions. Furthermore, extremal black holes turn out to be dual to "un-shrinkable" molecules of Van der Waals real fluid, which may explain their thermodynamical stability.