Thermodynamic response functions and Maxwell relations for a Kerr black hole

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.

25 pages, 13 figures