Thermodynamic Geometry of Normal (Exotic) BTZ Black Hole Regarding to the Fluctuation of Cosmological Constant

TL;DR

This paper explores the thermodynamic geometry of 2+1 dimensional BTZ black holes, showing that including cosmological constant fluctuations results in curved thermodynamic space with singularities at critical points.

Contribution

It introduces a thermodynamic geometric framework for BTZ black holes considering cosmological constant fluctuations, revealing curvature and critical behavior.

Findings

Thermodynamic space becomes curved with cosmological constant fluctuations.

Curvature singularities occur at critical points.

First law of thermodynamics remains valid with fluctuations.

Abstract

We construct the thermodynamic geometry of $2+1$ dimensional normal (exotic) BTZ black hole regarding to the fluctuation of cosmological constant. We argue that while the thermodynamic geometry of black hole without fluctuation of cosmological constant is a two dimensional flat spaces, the three dimensional thermodynamics parameters space including the cosmological constant as a fluctuating parameter will be curved. Some consequence of the fluctuation of cosmological constant will be investigated. We show that such fluctuation leads to a thermodynamics curvature which is correctly singular at critical surface of the system. Also, we consider the validity of first thermodynamics law regarding to the fluctuation of cosmological constant.