Geometrothermodynamics of phantom AdS black holes

TL;DR

This paper studies the thermodynamics of charged phantom AdS black holes by considering the cosmological constant as a variable, using both classical and geometrothermodynamics methods, and finds consistent results.

Contribution

It introduces a comprehensive analysis of phantom AdS black hole thermodynamics using extended phase space and compares classical and geometric approaches for the first time.

Findings

Thermodynamic properties depend on the cosmological constant as a variable.

Classical and geometrothermodynamics approaches yield compatible results.

Fundamental equations are homogeneous functions on an extended space.

Abstract

We show that to investigate the thermodynamic properties of charged phantom spherically symmetric anti-de-Sitter black holes, it is necessary to consider the cosmological constant as a thermodynamic variable so that the corresponding fundamental equation is a homogeneous function defined on an extended equilibrium space. We explore all the thermodynamic properties of this class of black holes by using the classical physical approach, based upon the analysis of the fundamental equation, and the alternative mathematical approach as proposed in geometrothermodynamics. We show that both approaches are compatible and lead to equivalent results.