Geometric description of BTZ black holes thermodynamics

Abstract

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 $2-$dimensional thermodynamic metric whose curvature is non-vanishing, 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.

References in corpus (8)

• Geometrothermodynamics
• Geometrothermodynamics of black holes
• Unified geometric description of black hole thermodynamics
• Flat Information Geometries in Black Hole Thermodynamics
• BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and Statistical Entropy
• A Commentary on Ruppeiner Metrics for Black Holes
• Ruppeiner theory of black hole thermodynamics
• Thermodynamic systems as bosonic strings

Cited by in corpus (3)

• Phase transitions in geometrothermodynamics
• Thermodynamic systems as extremal hypersurfaces
• Thermodynamic systems as bosonic strings