Bardeen Regular Black Hole With an Electric Source

TL;DR

This paper demonstrates that the Bardeen regular black hole solution can be interpreted as arising from Einstein equations with an electric source, expanding the understanding of regular black hole models in gravity theories.

Contribution

It shows that the Bardeen black hole can be modeled with an electric source, not just magnetic, and analyzes the associated energy conditions and Lagrangian behavior.

Findings

Bardeen black hole can be sourced electrically, not only magnetically.

Electric field in this model does not follow Coulomb's law.

Energy conditions are analyzed for the electric source case.

Abstract

If some energy conditions on the stress-energy tensor are violated, is possible construct regular black holes in General Relativity and in alternative theories of gravity. This type of solution has horizons but does not present singularities. The first regular black hole was presented by Bardeen and can be obtained from Einstein equations in the presence of an electromagnetic field. E. Ayon-Beato and A. Garcia reinterpreted the Bardeen metric as a magnetic solution of General Relativity coupled to a nonlinear electrodynamics. In this work show that the Bardeen model may also be interpreted as a solutions of Einstein equations in the presence of a electric source, whose electric field does not behaves as a Coulomb field. We analyzed the asymptotic forms of the Lagrangian for the electric case and also analyzed the energy conditions.