When Bumblebee Meets NLED: Lorentz-Violating Black Holes and Regular Spacetimes

TL;DR

This paper constructs charged black hole solutions in bumblebee gravity coupled with nonlinear electrodynamics, revealing conditions for regular, horizonless spacetimes that interpolate between AdS/dS cores and Lorentz-violating vacua.

Contribution

It introduces a method to obtain regular, horizonless solutions in Lorentz-violating gravity coupled with NLED, with specific fine-tuning of parameters to remove singularities.

Findings

Solutions are asymptotic to Lorentz-violating vacua with conical singularities.

Fine-tuning mass and charge can eliminate pole singularities, yielding marginally regular black holes.

Certain NLED theories like Born-Infeld allow complete removal of singularities with specific parameter relations.

Abstract

We construct charged black hole solutions in bumblebee gravity coupled to a general class of nonlinear electrodynamics (NLED) using an auxiliary Maxwell-scalar formalism. The norm-fixed radial configuration of the bumblebee vector makes the solutions asymptotic to a conical Lorentz-violating vacuum and requires stringent nonminimal bumblebee-NLED couplings. The general black hole solutions contain independent mass and charge parameters. There are two sources of singular behavior at the center: one is due to the Schwarzschild-type pole and the other is the residual conical singularity of the Lorentz-violating vacuum. By fine-tuning the mass-charge relation, one can generally remove the pole singularity, giving rise to marginally regular black holes. For a suitable NLED theory such as Born-Infeld theory, both singularity sources can be removed at the cost of requiring both the mass and the charge to be fine-tuned to specific functions of the coupling constants. The resulting solutions describe regular horizonless spacetimes interpolating from AdS or dS cores to Lorentz-violating vacua.