On the ensemble dependence in black hole geometrothermodynamics

Abstract

We investigate the dependence of thermodynamic properties of black holes on the choice of statistical ensemble for a particular class of Einstein-Maxwell-Gauss-Bonnet black holes with cosmological constant. We use partial Legendre transformations in the thermodynamic limit in order to compare the results in different ensembles, and show that the phase transition structure depend on the choice of thermodynamic potential. This result implies that thermodynamic metrics which are partially Legendre invariant cannot be employed to describe black hole thermodynamics, and partly explains why a particular thermodynamic metric has been used so far in the framework of black hole geometrothermodynamics.

14 pages, no figures

References in corpus (8)

• Geometrothermodynamics
• Unified geometric description of black hole thermodynamics
• Phase transitions in geometrothermodynamics
• Geometrothermodynamics of higher dimensional black holes
• Phase transition for black holes with scalar hair and topological black holes
• Thermodynamic systems as extremal hypersurfaces
• The conformal metric structure of Geometrothermodynamics
• Geometrothermodynamics of five dimensional black holes in Einstein-Gauss-Bonnet-theory

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