Geometrothermodynamics of five dimensional black holes in Einstein-Gauss-Bonnet-theory

TL;DR

This paper explores the thermodynamic behavior of five-dimensional black holes in various Einstein-Gauss-Bonnet theories using geometrothermodynamics, revealing divergences in thermodynamic curvature at critical points.

Contribution

It introduces a Legendre invariant metric in geometrothermodynamics for 5D black holes and compares different entropy formulations, highlighting their non-equivalence.

Findings

Thermodynamic curvature diverges at zero temperature and heat capacity divergence.

Different entropy approaches yield non-equivalent thermodynamic descriptions.

Geometrothermodynamics effectively identifies critical points in black hole thermodynamics.

Abstract

We investigate the thermodynamic properties of 5D static and spherically symmetric black holes in (i) Einstein-Maxwell-Gauss-Bonnet theory, (ii) Einstein-Maxwell-Gauss-Bonnet theory with negative cosmological constant, and in (iii) Einstein-Yang-Mills-Gauss-Bonnet theory. To formulate the thermodynamics of these black holes we use the Bekenstein-Hawking entropy relation and, alternatively, a modified entropy formula which follows from the first law of thermodynamics of black holes. The results of both approaches are not equivalent. Using the formalism of geometrothermodynamics, we introduce in the manifold of equilibrium states a Legendre invariant metric for each black hole and for each thermodynamic approach, and show that the thermodynamic curvature diverges at those points where the temperature vanishes and the heat capacity diverges.