Construction of Regular Black Holes in General Relativity

TL;DR

This paper develops a method to construct exact, regular black hole solutions with electric or magnetic charges in General Relativity coupled with nonlinear electrodynamics, including solutions with a cosmological constant.

Contribution

It introduces a general procedure for creating regular black hole solutions in Einstein gravity with nonlinear electrodynamics, extending to asymptotically anti-de Sitter spaces.

Findings

Regular black hole solutions without singularities.

Derived the first law of thermodynamics for these solutions.

Extended the method to include a cosmological constant.

Abstract

We present a general procedure for constructing exact black hole solutions with electric or magnetic charges in General Relativity coupled to a nonlinear electrodynamics. We obtain a variety of two-parameter family spherically symmetric black hole solutions. In particular, the singularity at the central of the space-time can be cancelled in the parameters space and the black hole solutions become regular everywhere in the space-time. We study the global properties of the solutions and derive the first law of thermodynamics. We also generalize the procedure to include a cosmological constant and construct regular black hole solutions that are asymptotic to anti-de Sitter space-time.