Thermodynamic Geometry and Locally Anisotropic Black Holes

TL;DR

This paper explores the thermodynamic geometry of a new class of (2+1)-dimensional locally anisotropic black holes with elliptical horizons, revealing critical points through curvature analysis.

Contribution

It introduces a novel thermodynamic geometric framework for anisotropic black holes with elliptical horizons in a Finsler-like spacetime.

Findings

Thermodynamic curvatures computed for anisotropic black holes.

Critical points identified where thermodynamic curvature vanishes.

Two geometric approaches analyzed for thermodynamic properties.

Abstract

Thermodynamic properties of locally anisotropic (2+1)-black holes are studied by applying geometric methods. We consider a new class of black holes with a constant in time elliptical event horizon which is imbedded in a generalized Finsler like spacetime geometry induced from Einstein gravity. The corresponding thermodymanic systems are three dimensional with entropy S being a hypersurface function on mass M, anisotropy angle $\theta$ and eccentricity of elliptic deformations $\epsilon$. Two-dimensional curved thermodynamic geometries for locally anistropic deformed black holes are constructed after integration on anisotropic parameter $\theta$. Two approaches, the first one based on two-dimensional hypersurface parametric geometry and the second one developed in a Ruppeiner-Mrugala-Janyszek fashion, are analyzed. The thermodynamic curvatures are computed and the critical points of curvature vanishing are defined.