Geometric description of BTZ black holes thermodynamics
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 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.
Keywords
Cite
@article{arxiv.0811.2524,
title = {Geometric description of BTZ black holes thermodynamics},
author = {Hernando Quevedo and Alberto Sanchez},
journal= {arXiv preprint arXiv:0811.2524},
year = {2009}
}