Regular Magnetic Black Holes and Monopoles from Nonlinear Electrodynamics

TL;DR

This paper explores regular magnetic black holes and monopoles within nonlinear electrodynamics coupled to general relativity, revealing conditions for their existence and analyzing their properties through duality techniques.

Contribution

It identifies conditions under which nonlinear electrodynamics produces regular magnetic black holes and monopoles, and compares magnetic solutions with electric ones using duality.

Findings

Regular solutions exist only with zero electric charge and finite L(F) at F→∞.

Magnetic solutions include black holes and monopoles with regular metrics.

Duality relates solutions of different NED theories, aiding comparison.

Abstract

It is shown that general relativity coupled to nonlinear electrodynamics (NED) with the Lagrangian $L(F)$, $F = F_mn F^mn$ having a correct weak field limit, leads to nontrivial static, spherically symmetric solutions with a globally regular metric if and only if the electric charge is zero and $L(F)$ tends to a finite limit as $F \to \infty$. Properties and examples of such solutions, which include magnetic black holes and soliton-like objects (monopoles), are discussed. Magnetic solutions are compared with their electric counterparts. A duality between solutions of different theories specified in two alternative formulations of NED (called $FP$ duality) is used as a tool for this comparison.