Existence conditions of nonsingular dyonic black holes in nonlinear electrodynamics

TL;DR

This paper derives conditions under which nonsingular dyonic black hole solutions exist in nonlinear electrodynamics coupled with general relativity, providing specific criteria and examples for such solutions.

Contribution

It establishes a criterion on the Lagrangian for the existence of nonsingular dyonic black holes and confirms this with explicit examples.

Findings

Derived a criterion for nonsingular dyonic black hole existence

Provided an example Lagrangian satisfying the criterion

Confirmed the existence of dyonic solutions in specific models

Abstract

General relativity coupled to nonlinear electrodynamics is known to have nonsingular black hole solutions. We investigate the existence conditions for such solutions in two-parameter Lagrangian ${\cal L} \left( {\cal F} , {\cal G} \right)$. In particular, we obtain a criterion on the Lagrangian for the existence of nonsingular black hole with a dyonic charge. In addition, we present a simple example of two-parameter Lagrangian satisfying the criterion, in which the existence of the dyonic solution is actually confirmed. Moreover, apart from the actual existence of dyonic solutions, we consider some examples for the Lagrangian satisfying such a criterion.