Singularities in General Relativity coupled to nonlinear electrodynamics

TL;DR

This paper investigates how nonlinear electrodynamics influences photon propagation in regular black hole spacetimes, revealing the existence of effective geometric singularities that can be hidden or exposed depending on parameters.

Contribution

It demonstrates the presence of singularities in the effective geometry of photons in regular black holes with nonlinear electrodynamics, a novel insight into their causal structure.

Findings

Effective geometry singularities can be hidden or naked.

Photon propagation is affected by electromagnetic nonlinearities.

Unusual properties of regular black hole solutions are identified.

Abstract

We study here some consequences of the nonlinearities of the electromagnetic field acting as a source of Einstein's equations on the propagation of photons. We restrict to the particular case of a ``regular black hole'', and show that there exist singularities in the effective geometry. These singularities may be hidden behind a horizon or naked, according to the value of a parameter. Some unusual properties of this solution are also analyzed.