Rotating regular black holes

TL;DR

This paper extends non-rotating regular black hole models to include rotation using the Newman-Janis algorithm, resulting in new solutions that are singularity-free and have specific physical properties relevant for astrophysical observations.

Contribution

It introduces rotating regular black hole solutions derived from Hayward and Bardeen metrics, filling a gap in models that include black hole spin.

Findings

Solutions are Petrov type D and singularity-free.

Some solutions violate the weak energy condition at non-zero spin.

Curvature invariants vary at the origin depending on the approach.

Abstract

The formation of spacetime singularities is a quite common phenomenon in General Relativity and it is regulated by specific theorems. It is widely believed that spacetime singularities do not exist in Nature, but that they represent a limitation of the classical theory. While we do not yet have any solid theory of quantum gravity, toy models of black hole solutions without singularities have been proposed. So far, there are only non-rotating regular black holes in the literature. These metrics can be hardly tested by astrophysical observations, as the black hole spin plays a fundamental role in any astrophysical process. In this letter, we apply the Newman-Janis algorithm to the Hayward and to the Bardeen black hole metrics. In both cases, we obtain a family of rotating solutions. Every solution corresponds to a different matter configuration. Each family has one solution with special properties, which can be written in Kerr-like form in Boyer-Lindquist coordinates. These special solutions are of Petrov type D, they are singularity free, but they violate the weak energy condition for a non-vanishing spin and their curvature invariants have different values at $r=0$ depending on the way one approaches the origin. We propose a natural prescription to have rotating solutions with a minimal violation of the weak energy condition and without the questionable property of the curvature invariants at the origin.