Thermodynamic Metrics and Black Hole Physics

TL;DR

This paper surveys thermodynamic metrics, especially the Hessian of entropy, and explores their application to black hole thermodynamics, focusing on Kerr and Kerr-Newman black holes and their global properties.

Contribution

It provides a detailed analysis of the Gibbs surface of Kerr black holes, including the inner horizon entropy, extending previous thermodynamic geometric studies.

Findings

Analysis of the global properties of the Kerr black hole Gibbs surface

Extension of thermodynamic metrics to include inner horizon entropy

Discussion of thermodynamic geometry in Kerr-Newman black holes

Abstract

We give a brief survey of thermodynamic metrics, in particular the Hessian of the entropy function, and how they apply to black hole thermodynamics. We then provide a detailed discussion of the Gibbs surface of Kerr black holes. In particular we analyze its global properties, and extend it to take the entropy of the inner horizon into account. A brief discussion of Kerr-Newman black holes is included.