Geometrothermodynamics of asymptotically anti - de Sitter black holes

Details Geometrothermodynamics of asymptotically anti - de Sitter black holes Geometrothermodynamics of asymptotically anti - de Sitter black holes

2008-05-20

arxiv.org/abs/0805.3003v2

JHEP 0809:034,2008

Physics

High Energy Physics

High Energy Physics - Theory

Section on statistical ensembles and new references added

Scientific paper

10.1088/1126-6708/2008/09/034

We apply the formalism of geometrothermodynamics to the case of black holes with cosmological constant in four and higher dimensions. We use a thermodynamic metric which is invariant with respect to Legendre transformations and determines the geometry of the space of equilibrium states. For all known black holes in higher dimensions, we show that the curvature scalar of the thermodynamic metric in all the cases is proportional to the heat capacity. As a consequence, phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as true curvature singularities. We interpret this as a further indication that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.

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