Thermodynamic properties of asymptotically Reissner-Nordstrom black holes

TL;DR

This paper explores the thermodynamic properties of asymptotically Reissner-Nordstrom black holes influenced by nonlinear electrodynamics, revealing how nonlinearity impacts stability and phase transition points.

Contribution

It provides exact solutions for black holes with nonlinear electrodynamics and analyzes their thermodynamics using Geometrothermodynamics, linking singularities to Davies points.

Findings

Nonlinearity affects the minimum stable black hole size.

Heat capacity calculations show stability conditions.

Ricci scalar divergences correspond to phase transition points.

Abstract

Motivated by possible relation between Born-Infeld type nonlinear electrodynamics and an effective low-energy action of open string theory, asymptotically Reissner--Nordstrom black holes whose electric field is described by a nonlinear electrodynamics (NLED) are studied. We take into account a four dimensional topological static black hole ansatz and solve the field equations, exactly, in terms of the NLED as a matter field. The main goal of this paper is investigation of thermodynamic properties of the obtained black holes. Moreover, we calculate the heat capacity and find that the nonlinearity affects the minimum size of stable black holes. We also use Legendre-invariant metric proposed by Quevedo to obtain scalar curvature divergences. We find that the singularities of the Ricci scalar in Geometrothermodynamics (GTD) method take place at the Davies points.