Black hole thermodynamics in the presence of nonlinear electromagnetic fields

TL;DR

This paper extends black hole thermodynamics to include nonlinear electromagnetic fields, deriving generalized laws and exploring their implications for black hole mechanics and energy conditions.

Contribution

It introduces a generalized first law of black hole mechanics incorporating nonlinear electrodynamics with detailed derivations and analysis.

Findings

Generalized first law for black holes with nonlinear electromagnetic fields

Discussion of energy conditions and zeroth law validity

Analysis of the generalized Smarr formula and its properties

Abstract

As the interaction between the black holes and highly energetic infalling charged matter receives quantum corrections, the basic laws of black hole mechanics have to be carefully rederived. Using the covariant phase space formalism, we generalize the first law of black hole mechanics, both "equilibrium state" and "physical process" versions, in the presence of nonlinear electrodynamics fields, defined by Lagrangians depending on both quadratic electromagnetic invariants, $F_{ab}F^{ab}$ and $F_{ab}\,{\star F}^{ab}$. Derivation of this law demands a specific treatment of the Lagrangian parameters, similar to embedding of the cosmological constant into thermodynamic context. Furthermore, we discuss the validity of energy conditions, several complementing proofs of the zeroth law of black hole electrodynamics and some aspects of the recently generalized Smarr formula, its (non-)linearity and relation to the first law.