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Geometrothermodynamics of black holes

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Abstract

The thermodynamics of black holes is reformulated within the context of the recently developed formalism of geometrothermodynamics. This reformulation is shown to be invariant with respect to Legendre transformations, and to allow several equivalent representations. Legendre invariance allows us to explain a series of contradictory results known in the literature from the use of Weinhold’s and Ruppeiner’s thermodynamic metrics for black holes. For the Reissner–Nordström black hole the geometry of the space of equilibrium states is curved, showing a non trivial thermodynamic interaction, and the curvature contains information about critical points and phase transitions. On the contrary, for the Kerr black hole the geometry is flat and does not explain its phase transition structure.

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  1. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, 04510, Mexico D.F., Mexico

    Hernando Quevedo

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  1. Hernando Quevedo
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Quevedo, H. Geometrothermodynamics of black holes. Gen Relativ Gravit 40, 971–984 (2008). https://doi.org/10.1007/s10714-007-0586-0

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