Existence conditions of nonsingular dyonic black holes in nonlinear electrodynamics

Abstract We study the conditions under which nonsingular black hole solutions can exist in General relativity coupled to nonlinear electrodynamics, focusing on Lagrangians that depend on two electromagnetic invariants F and G . In particular, we derive a necessary criterion that the Lagrangian L ( F , G ) must satisfy for static, spherically symmetric dyonic black hole solutions to exist without curvature singularities. We demonstrate that this criterion is consistent with known no-go theorems for one-parameter Lagrangians L ( F ) , while allowing for new possibilities in two-parameter models. As an explicit example, we construct a simple Lagrangian that satisfies the criterion and supports a nonsingular dyonic configuration. We also present several additional models that satisfy the criterion, which may serve as possible candidates for supporting nonsingular dyonic solutions.