Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamics

TL;DR

This paper investigates the thermodynamic properties of electrically charged black holes in three-dimensional nonlinear electrodynamics coupled with gravity, classifying models and deriving universal scaling laws for their thermodynamic variables.

Contribution

It provides a comprehensive classification of admissible nonlinear electrodynamics models in flat space and extends thermodynamic laws to their associated black hole solutions, revealing universal scaling behaviors.

Findings

Classified twelve families of admissible models based on flat space properties.

Derived universal scaling laws for thermodynamic variables across all solutions.

Extended thermodynamic laws to black holes in nonlinear electrodynamics with consistent behaviors.

Abstract

We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition, defines twelve families of admissible models. When these models are coupled to gravity, the flat space classification leads to a complete characterization of the associated sets of gravitating electrostatic spherically symmetric solutions by their central and asymptotic behaviours. We focus on nine of these families, which support asymptotically Schwarzschild-like black hole configurations, for which the thermodynamic analysis is possible and pertinent. In this way, the thermodynamic laws are extended to the sets of black hole solutions of these families, for which the generic behaviours of the relevant state variables are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we find universal scaling laws (which hold and are the same for all the black hole solutions of models belonging to any of the nine families) running the thermodynamic variables with the electric charge and the horizon radius. These scale transformations form a one-parameter multiplicative group, leading to universal "renormalization group"-like first-order differential equations. The beams of characteristics of these equations generate the full set of black hole states associated to any of these gravitating nonlinear electrodynamics...