Thermodynamic response functions and Maxwell relations for a Kerr black hole

TL;DR

This paper develops a thermodynamic framework for Kerr black holes, introducing new response functions, Maxwell relations, and stability analysis, revealing analogies with magnetic systems and identifying conditions for stability.

Contribution

It presents novel thermodynamic response functions and Maxwell relations for Kerr black holes, establishing a mathematical analogy with magnetic systems and analyzing stability conditions.

Findings

Identified regions of local thermodynamic stability and instability.

Derived Maxwell relations and thermodynamic squares for black holes.

Established analogy between black hole thermodynamics and magnetic systems.

Abstract

Assuming the existence of a fundamental thermodynamic relation, the classical thermodynamics of a black hole with mass and angular momentum is given. New definitions of response functions and $TdS$ equations are introduced and mathematical analogous of the Euler equation and Gibbs-Duhem relation are founded. Thermodynamic stability is studied from concavity conditions, resulting in an unstable equilibrium at all the domain except for a region of local stable equilibrium. Maxwell relations are written, allowing to build the thermodynamic squares. Our results shown an interesting analogy between thermodynamics of gravitational and magnetic systems.