Constraints on singularity resolution by nonlinear electrodynamics

TL;DR

This paper investigates whether nonlinear electrodynamics can resolve black hole singularities and finds that extending the theory to include additional invariants does not overcome existing constraints that prevent regular solutions.

Contribution

It extends Bronnikov's no-go theorems by considering more general Lagrangians depending on two electromagnetic invariants, showing the limitations in resolving singularities.

Findings

Adding the second electromagnetic invariant does not allow regular black hole solutions.

The tension between Maxwellian weak field limit and bounded curvature persists.

Constraints on nonlinear electrodynamics prevent singularity resolution in these models.

Abstract

One of the long standing problems is a quest for regular black hole solutions, in which a resolution of the spacetime singularity has been achieved by some physically reasonable, classical field, before one resorts to the quantum gravity. The prospect of using nonlinear electromagnetic fields for this goal has been limited by the Bronnikov's no-go theorems, focused on Lagrangians depending on the electromagnetic invariant $F_{ab}F^{ab}$ only. We extend Bronnikov's results by taking into account Lagrangians that depend on both electromagnetic invariants, $F_{ab}F^{ab}$ and $F_{ab}\,{\star F^{ab}}$, and prove that the tension between the Lagrangian's Maxwellian weak field limit and boundedness of the curvature invariants persists in more general class of theories.