Investigación

 

Thermodynamic response functions and Maxwell relations for a Kerr black hole

 

L. Escamilla and J. Torres-Arenas

 

División de Ciencias e Ingenierías Campus León, Universidad de Guanajuato, Loma del Bosque 103, 37150 León Guanajuato, México, e-mail: lescamilla@fisica.ugto.mx; jtorres@fisica.ugto.mx

 

Received 18 February 2013.
Accepted 4 October 2013.

 

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 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.

Keywords: Thermodynamics; black holes; long range interactions.

 

PACS: 05.70.-a; 04.70.Bw; 95.30.Tg

 

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Acknowledgments

We want to acknoweledge CONACyT (proyect-152684) and the University of Guanajuato (DAIP-006/10) for the support in the realization of this work.

 

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