Regular black holes: Electrically charged solutions, Reissner-Nordstr\"om outside a de Sitter core

TL;DR

This paper constructs and analyzes regular charged black hole solutions in general relativity, featuring a de Sitter interior, Reissner-Nordström exterior, and a charged matter boundary, addressing singularity issues in classical black hole models.

Contribution

It introduces new regular black hole solutions with charged matter and de Sitter cores, expanding understanding of non-singular black hole models within Einstein-Maxwell theory.

Findings

Existence of regular nonextremal black holes with null matter boundary

Presence of regular extremal black holes with timelike matter boundary

Identification of overcharged star solutions with timelike matter boundary

Abstract

To have the correct picture of a black hole as a whole it is of crucial importance to understand its interior. The singularities that lurk inside the horizon of the usual Kerr-Newman family of black hole solutions signal an endpoint to the physical laws and as such should be substituted in one way or another. A proposal that has been around for sometime, is to replace the singular region of the spacetime by a region containing some form of matter or false vacuum configuration that can also cohabit with the black hole interior. Black holes without singularities are called regular black holes. In the present work regular black hole solutions are found within general relativity coupled to Maxwell's electromagnetism and charged matter. We show that there are objects which correspond to regular charged black holes, whose interior region is de Sitter, whose exterior region is Reissner-Nordstr\"om, and the boundary between both regions is made of an electrically charged spherically symmetric coat. There are several type of solutions: regular nonextremal black holes with a null matter boundary, regular nonextremal black holes with a timelike matter boundary, regular extremal black holes with a timelike matter boundary, and regular overcharged stars with a timelike matter boundary. The main physical and geometrical properties of such charged regular solutions are analysed.