On the compatibility of Nonlinear Electrodynamics models with Robinson--Trautman geometry

TL;DR

This paper examines the compatibility of various nonlinear electrodynamics models with Robinson--Trautman geometries, highlighting the unique suitability of Maxwell's theory and the limitations of regular black hole models within this class.

Contribution

It provides a detailed analysis of nonlinear electrodynamics models in Robinson--Trautman spacetimes, emphasizing the uniqueness of Maxwell theory and differences between L(F) and L(F,G) models.

Findings

Maxwell electrodynamics uniquely compatible with Robinson--Trautman class.

Regular black hole models are incompatible with Robinson--Trautman solutions.

Born--Infeld model shows distinct behavior for electric fields with magnetic charges.

Abstract

Robinson--Trautman solutions with Nonlinear Electrodynamics are investigated for both L(F ) and L(F, G) Lagrangians and presence of electric and magnetic charges as well as electromagnetic radiation is assumed. Particular interest is devoted to models representing regular black holes for spherically symmetric situations. The results show clear uniqueness of Maxwell electrodynamics with respect to compatibility with Robinson--Trautman class. Additionally, regular black hole models are clearly not suited to this class while famous Born--Infeld model illustrates important distinction between L(F ) and L(F, G) for obtained electric field when magnetic field is nontrivial.