Dyonic configurations in nonlinear electrodynamics coupled to general relativity

TL;DR

This paper develops a general method to find dyonic solutions in nonlinear electrodynamics coupled with general relativity, including explicit solutions for the Born-Infeld theory and special cases with self-dual fields.

Contribution

It introduces a new scheme for deriving dyonic solutions in nonlinear electrodynamics coupled to gravity, expressed in terms of the invariant-dependent radial coordinate.

Findings

Derived a general quadrature scheme for dyonic solutions

Obtained explicit solutions for Born-Infeld theory

Identified a self-dual electromagnetic field case with Reissner-Nordström metric

Abstract

We consider static, spherically symmetric configurations in general relativity, supported by nonlinear electromagnetic fields with gauge-invariant Lagrangians depending on the single invariant $f = F_{\mu\nu} F^{\mu\nu}$. After a brief review on black hole (BH) and solitonic solutions, obtained so far with pure electric or magnetic fields, an attempt is made to obtain dyonic solutions, those with both electric and magnetic charges. A general scheme is suggested, leading to solutions in quadratures for an arbitrary Lagrangian function $L(f)$ (up to some monotonicity restrictions); such solutions are expressed in terms of $f$ as a new radial coordinate instead of the usual coordinate $r$. For the truncated Born-Infeld theory (depending on the invariant $f$ only), a general dyonic solution is obtained in terms of $r$. A feature of interest in this solution is the existence of a special case with a self-dual electromagnetic field, $f \equiv 0$ and the Reissner-Nordstr\"om metric.