Thermodynamics, geometrothermodynamics and critical behavior of (2+1)-dimensional black holes

TL;DR

This paper explores the thermodynamic and phase transition properties of (2+1)-dimensional black holes using geometrothermodynamics, demonstrating that curvature scalar analysis accurately indicates phase transition points.

Contribution

It introduces a Legendre invariant metric approach to analyze black hole thermodynamics, revealing phase transition behavior through curvature scalar analysis.

Findings

Curvature scalar signals phase transition points.

Legendre invariant metric accurately models thermodynamic interactions.

Black holes exhibit curved thermodynamic geometry.

Abstract

In this paper, we study the properties of the (2+1)-dimensional black holes from the viewpoint of geometrothermodynamics. We show that the Legendre invariant metric of the (2+1)-dimensional black holes can produce correctly the behavior of the thermodynamic interaction and phase transition structure of the corresponding black hole configurations. We find that they are both curved and the curvature scalar gives the information about the phase transition point.