Geometric Thermodynamics of Schwarzschild-AdS black hole with a Cosmological Constant as State Variable

TL;DR

This paper applies geometrothermodynamics to Schwarzschild-AdS black holes, showing that the entropy representation captures the Hawking-Page phase transition through divergence in thermodynamic curvature, unlike other representations.

Contribution

It demonstrates the effectiveness of the entropy representation in geometrothermodynamics for reproducing black hole phase transitions.

Findings

Hawking-Page transition identified as curvature divergence in entropy representation

Enthalpy and total energy representations do not reproduce the phase transition

Geometrothermodynamics provides a geometric perspective on black hole thermodynamics

Abstract

The thermodynamics of the Schwarzschild-AdS black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD). Different choices of the metric in the equilibrium states manifold are used in order to reproduce the Hawking-Page phase transition as a divergence of the thermodynamical curvature scalar. We show that the enthalpy and total energy representations of GTD does not reproduce the transition while the entropy rep- resentation gives the expected behavior.