On gravitating dyonic configurations in nonlinear electrodynamics

TL;DR

This paper explores static, spherically symmetric dyonic configurations in nonlinear electrodynamics coupled with gravity, revealing solutions where the electromagnetic invariant is zero everywhere for equal electric and magnetic charges.

Contribution

It demonstrates the existence of solutions with zero electromagnetic invariant in dyonic systems with equal charges across various gravity theories, extending known solutions.

Findings

Existence of solutions with zero invariant f for equal electric and magnetic charges.

Such solutions are valid in GR and extended gravity theories like scalar-tensor and F(R) gravity.

The solutions simplify the behavior of nonlinear electromagnetic fields in these theories.

Abstract

We consider static, spherically symmetric configurations of nonlinear electromagnetic fields with Lagrangians $L(f)$, where $f = F_{\mu\nu} F^{\mu\nu}$, in general relativity (GR) and other metric theories of gravity. The corresponding exact solutions are well known in the framework of GR in cases where only an electric charge ($q_e$) or a magnetic charge ($q_m$) are present, but only a few solutions in particular examples of $L(f)$ are known for dyonic systems with both nonzero $q_e$ and $q_m$. We study the properties of such systems in the special case of equal electric and magnetic charges and, assuming a correct Maxwell limit of $L(f)$, show that there always exists such a configuration of the electromagnetic field that the invariant $f$ is zero in the whole space. It leads to the existence of the corresponding families of solutions both in GR in the presence of other sources of gravity (like fluids or scalar fields) and in a wide range of extended theories of gravity (e.g., scalar-tensor and $F(R)$ gravity), in which the nonlinear electromagnetic field behaves in an especially simple manner.