Regular Sources of the Kerr-Schild class for Rotating and Nonrotating Black Hole Solutions

TL;DR

This paper presents a unified Kerr-Schild metric framework for modeling regular, smooth-core black hole interiors, including rotating and nonrotating cases, with specific core structures like de Sitter and anti-de Sitter regions, and addresses singularity regularization.

Contribution

It introduces a unified approach using Kerr-Schild metrics to model regular black hole interiors with smooth matter distributions, covering both rotating and nonrotating solutions.

Findings

De Sitter cores can be integrated into Schwarzschild black holes.

Rotating black holes can have anisotropic, rotating de Sitter-like cores.

Charged black holes' sources resemble 'bags' with de Sitter or anti-de Sitter interiors.

Abstract

A unified approach to regular interiors of black holes with smooth matter distributions in the core region is given. The approach is based on a class of Kerr-Schild metrics representing minimal deformations of the Kerr-Newman solution, and allows us to give a common treatment for (charged and uncharged) rotating and nonrotating black holes. It is shown that the requirement of smoothness of the source constraints the structure of the core region in many respects: in particular, for Schwarzschild holes a de Sitter core can be selected, which is surrounded by a smooth shell giving a leading contribution to the total mass of the source. In the rotating, noncharged case the source has a similar structure, taking the form of a (anisotropic and rotating) de Sitter-like core surrounded by a rotating elliptic shell. The Kerr singular ring is regularized by anisotropic matter rotating in the equatorial plane, so that the negative sheet of the Kerr geometry is absent. In the charged case the sources take the form of ``bags'', which can have de Sitter or anti de Sitter interiors and a smooth domain wall boundary, with a tangential stress providing charge confinement. The ADM and Tolman relations are used to calculate the total mass of the sources.