Slowly rotating regular black holes with a charged thin shell

TL;DR

This paper constructs slowly rotating regular black hole solutions with a charged thin shell, analyzing the effects of rotation on the shell's stress tensor and matching conditions, and numerically investigates these effects on a specific regular black hole model.

Contribution

It introduces a method to model slowly rotating regular black holes with a charged thin shell and analyzes the stress tensor and matching conditions under rotation.

Findings

The thin shell generally has anisotropic pressure when rotation is considered.

The thin shell can be a perfect fluid with isotropic pressure with appropriate matching.

Numerical analysis shows rotational effects on a specific regular black hole model.

Abstract

We obtain rotating solutions of regular black holes which are constructed of de Sitter spacetime with the axisymmetric stationary perturbation within the timelike charged thin shell and the Kerr-Newman geometry with sufficiently small rotation outside the shell. To treat the slowly rotating thin shell, we employ the method developed by de la Cruz and Israel. The thin shell is assumed to be composed of a dust in the zero-rotation limit and located inside the inner horizon of the black hole solution. We expand the perturbation in powers of the rotation parameter of the Kerr-Newman metric up to the second order. It is found that with the present treatment, the stress tensor of the thin shell in general has anisotropic pressure, i.e., the thin shell cannot be composed of a dust if the rotational effects are taken into account. However, the thin shell can be composed of a perfect fluid with isotropic pressure if the degrees of freedom appearing in the physically acceptable matching of the two distinct spacetimes are suitably used. We numerically investigate the rotational effects on the spherically symmetric charged regular black hole obtained by Uchikata, Yoshida and Futamase in detail.