Nonlinear electrodynamics, regular black holes and wormholes

TL;DR

This paper explores solutions in general relativity supported by nonlinear electromagnetic fields, revealing conditions for nonsingular magnetic black holes and wormholes, including an analytic solution for a specific nonlinear theory.

Contribution

It introduces a general framework for spherically symmetric solutions with nonlinear electrodynamics, including a new class of time-dependent wormholes without Maxwell limits.

Findings

Pure magnetic solutions can be completely nonsingular.

Analytic solutions are obtained for the truncated Born-Infeld theory.

Time-dependent wormholes exist only for specific nonlinear Lagrangians.

Abstract

We consider spherically symmetric configurations in general relativity, supported by nonlinear electromagnetic fields with gauge-invariant Lagrangians depending on the single invariant $f = F_{\mu\nu} F^{\mu\nu}$. Static black hole and solitonic solutions are briefly described, both with only an electric or magnetic charge and with both nonzero charges (the dyonic ones). It is stressed that only pure magnetic solutions can be completely nonsingular. For dyonic systems, apart from a general scheme of obtaining solutions in quadratures for an arbitrary Lagrangian function $L(f)$, an analytic solution is found for the truncated Born-Infeld theory (depending on the invariant $f$ only). Furthermore, considering spherically symmetric metrics with two independent functions of time, we find a natural generalization of the class of wormholes found previously by Arellano and Lobo with a time-dependent conformal factor. Such wormholes are shown to be only possible for some particular choices of the function $L(f)$, having no Maxwell weak-field limit.