Correspondence of phase transition points and singularities of thermodynamic geometry of black holes

TL;DR

This paper establishes a precise link between phase transition points and singularities in the thermodynamic geometry of black holes, demonstrating a universal correspondence applicable to various thermodynamic systems.

Contribution

It proves that divergences in specific heat align exactly with singularities in thermodynamic curvature for black holes, extending the formulation to general thermodynamic systems.

Findings

Divergent points of specific heat match thermodynamic curvature singularities.

The correspondence holds for different types of black holes.

The formulation is applicable to arbitrary thermodynamic systems.

Abstract

We explore a formulation of thermodynamic geometry of black holes and prove that the divergent points of the specific heat correspond exactly to the singularities of the thermodynamic curvature. We investigate this correspondence for different types of black holes. This formulation can also be applied to an arbitrary thermodynamic system.