Thermodynamics of charged black holes with a nonlinear electrodynamics source

TL;DR

This paper investigates the thermodynamics of charged black holes in nonlinear electrodynamics coupled to gravity, revealing diverse asymptotic behaviors, a generalized Smarr formula, and phase transitions distinct from Reissner-Nordstrom black holes.

Contribution

It introduces a comprehensive analysis of black hole thermodynamics in nonlinear electrodynamics with a new generalized Smarr formula and phase transition insights.

Findings

Finite mass and charge for all solutions

Generalized Smarr formula matches asymptotic behaviors

Existence of a first-order phase transition

Abstract

We study the thermodynamical properties of electrically charged black hole solutions of a nonlinear electrodynamics theory defined by a power p of the Maxwell invariant, which is coupled to Einstein gravity in four and higher spacetime dimensions. Depending on the range of the parameter p, these solutions present different asymptotic behaviors. We compute the Euclidean action with the appropriate boundary term in the grand canonical ensemble. The thermodynamical quantities are identified and in particular, the mass and the charge are shown to be finite for all classes of solutions. Interestingly, a generalized Smarr formula is derived and it is shown that this latter encodes perfectly the different asymptotic behaviors of the black hole solutions. The local stability is analyzed by computing the heat capacity and the electrical permittivity and we find that a set of small black holes are locally stable. In contrast to the standard Reissner-Nordstrom solution, there is a first-order phase transition between a class of these non-linear charged black holes and the Minkowski spacetime.