Thermodynamic Geometry and Locally Anisotropic Black Holes

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 $θ$ and eccentricity of elliptic deformations $ε$. Two-dimensional curved thermodynamic geometries for locally anistropic deformed black holes are constructed after integration on anisotropic parameter $θ$. 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.