Geometric description of BTZ black holes thermodynamics

TL;DR

This paper applies geometrothermodynamics to analyze the thermodynamic properties of BTZ black holes and their generalizations, revealing insights into thermodynamic interactions and phase transition absence.

Contribution

It introduces a thermodynamic metric for BTZ black holes and their extensions, showing non-zero curvature indicating interactions and no phase transitions.

Findings

Thermodynamic curvature is non-zero, indicating interaction.

No singularities imply absence of phase transitions.

Logarithmic entropy corrections correspond to curvature adjustments.

Abstract

We study the properties of the space of thermodynamic equilibrium states of the Ba\~nados-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.