On the Thermodynamic Geometry of BTZ Black Holes

TL;DR

This paper explores the thermodynamic geometry of BTZ black holes, revealing flat geometry in certain cases and curvature induced by thermal fluctuations, with implications for understanding black hole thermodynamics.

Contribution

It demonstrates the flatness of thermodynamic geometry for specific BTZ black holes and shows how thermal fluctuations introduce curvature, extending previous thermodynamic analyses.

Findings

Thermodynamic geometry is flat for rotating BTZ and BTZ Chern Simons black holes.

Thermal fluctuations induce non-zero scalar curvature in the thermodynamic geometry.

Leading logarithmic corrections to entropy are reproduced by including thermal fluctuations.

Abstract

We investigate the Ruppeiner geometry of the thermodynamic state space of a general class of BTZ black holes. It is shown that the thermodynamic geometry is flat for both the rotating BTZ and the BTZ Chern Simons black holes in the canonical ensemble. We further investigate the inclusion of thermal fluctuations to the canonical entropy of the BTZ Chern Simons black holes and show that the leading logartithmic correction due to Carlip is reproduced. We establish that the inclusion of thermal fluctuations induces a non zero scalar curvature to the thermodynamic geometry.