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Geometric description of BTZ black hole thermodynamics. (English) Zbl 1222.83113

Summary: We study the properties of the space of thermodynamic equilibrium states of the Bañados-Teitelboim-Zanelli (BTZ) black hole in \((2+1)\) gravity. We use the formalism of geometrothermodynamics to introduce in the space of equilibrium states a two-dimensional thermodynamic metric whose curvature is nonvanishing, indicating the presence of thermodynamic interaction, and free of singularities, indicating the absence of phase transitions. Similar results are obtained for generalizations of the BTZ black hole which include a Chern-Simons term and a dilatonic field. Small logarithmic corrections of the entropy turn out to be represented by small corrections of the thermodynamic curvature, reinforcing the idea that thermodynamic curvature is a measure of thermodynamic interaction.

MSC:

83C57 Black holes
81T20 Quantum field theory on curved space or space-time backgrounds
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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