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 the 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. The Maxwell relations are written, allowing to build the thermodynamic squares. Our results shown an interesting analogy between thermodynamics of gravitational and magnetic systems.
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[v1] 2013-10-28 17:05:27
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