Thermodynamic Geometry Of Charged Rotating BTZ Black Holes

TL;DR

This paper explores the thermodynamic properties and geometric descriptions of charged rotating BTZ black holes in (2+1)-gravity, highlighting the advantages of geometrothermodynamics over traditional geometries.

Contribution

It demonstrates that geometrothermodynamics provides a consistent, invariant framework for analyzing the thermodynamics of charged rotating BTZ black holes, unlike Weinhold and Ruppeiner geometries.

Findings

Weinhold and Ruppeiner geometries fail to fully describe the thermodynamics.

GTD successfully captures the thermodynamic behavior and limits of the black holes.

GTD offers a Legendre invariant approach for black hole thermodynamics.

Abstract

We study the thermodynamics and the thermodynamic geometries of charged rotating BTZ (CR-BTZ) black holes in (2+1)-gravity. We investigate the thermodynamics of these systems within the context of the Weinhold and Ruppeiner thermodynamic geometries and the recently developed formalism of geometrothermodynamics (GTD). Considering the behavior of the heat capacity and the Hawking temperature, we show that Weinhold and Ruppeiner geometries cannot describe completely the thermodynamics of these black holes and of their limiting case of vanishing electric charge. In contrast, the Legendre invariance imposed on the metric in GTD allows one to describe the CR-BTZ black holes and their limiting cases in a consistent and invariant manner.