Unified geometric description of black hole thermodynamics

TL;DR

This paper introduces a Legendre invariant metric in the thermodynamic state space of black holes, linking curvature singularities to phase transitions across various black hole types, providing a unified geometric framework.

Contribution

It presents a novel geometric approach using a Legendre invariant metric to describe black hole thermodynamics and phase transitions.

Findings

Curvature singularities correspond to phase transitions.

The approach applies to Kerr-Newman black holes and special cases.

Provides a unified geometric description of black hole thermodynamics.

Abstract

In the space of thermodynamic equilibrium states we introduce a Legendre invariant metric which contains all the information about the thermodynamics of black holes. The curvature of this thermodynamic metric becomes singular at those points where, according to the analysis of the heat capacities, phase transitions occur. This result is valid for the Kerr-Newman black hole and all its special cases and, therefore, provides a unified description of black hole phase transitions in terms of curvature singularities.