Geometrothermodynamics of asymptotically anti - de Sitter black holes

TL;DR

This paper applies geometrothermodynamics to asymptotically anti-de Sitter black holes, showing that the thermodynamic curvature scalar correlates with heat capacity and phase transitions, indicating thermodynamic interactions.

Contribution

It demonstrates that the thermodynamic curvature in geometrothermodynamics accurately reflects phase transitions and thermodynamic interactions in higher-dimensional AdS black holes.

Findings

Curvature scalar is proportional to heat capacity.

Phase transitions correspond to curvature singularities.

Thermodynamic interaction is measured by the curvature.

Abstract

We apply the formalism of geometrothermodynamics to the case of black holes with cosmological constant in four and higher dimensions. We use a thermodynamic metric which is invariant with respect to Legendre transformations and determines the geometry of the space of equilibrium states. For all known black holes in higher dimensions, we show that the curvature scalar of the thermodynamic metric in all the cases is proportional to the heat capacity. As a consequence, phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as true curvature singularities. We interpret this as a further indication that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.