Ruppeiner theory of black hole thermodynamics

TL;DR

This paper explores the geometric thermodynamics of black holes using Ruppeiner metrics across various gravity theories, revealing insights into their equilibrium states and thermodynamic properties.

Contribution

It applies Ruppeiner geometry to different black hole solutions, providing a unified geometric framework for understanding black hole thermodynamics.

Findings

Ruppeiner metrics reveal thermodynamic stability regions

Geometric structures differ across gravity theories

Insights into phase transitions of black holes

Abstract

The Ruppeiner metric as determined by the Hessian of the Gibbs surface provides a geometric description of thermodynamic systems in equilibrium. An interesting example is a black hole in equilibrium with its own Hawking radiation. In this article, we present results from the Ruppeiner study of various black hole families from different gravity theories e.g. 2D dilaton gravity, BTZ, general relativity and higher-dimensional Einstein-Maxwell gravity.