Studying KARMA (Kerr And Relativistic Matter Around)

TL;DR

This paper constructs and analyzes rotating black hole solutions with matter in various backgrounds, exploring their properties, singularities, and limits, including non-stationary and Vaidya-type generalizations.

Contribution

It introduces new solutions for Kerr-like black holes with matter, applying symmetry, singularity, and energy condition analyses, and extends to non-stationary and Vaidya-type cases.

Findings

Solutions exhibit pole singularities and bipolar outflows.

Constraints on matter content derived from energy conditions.

Generalizations include Kerr-Vaidya black holes.

Abstract

We construct series of solutions for the Kerr-type rotating black hole with non-trivial matter in flat and (A)dS backgrounds. Symmetry arguments and singularity analysis in the proposed black hole models fix the free parameters of the solutions, and the study of popular energy conditions makes it possible to impose constraints on configuration and field content of external matter. The resulted geometry of spacetimes is featured by a special type singularity in the north and south pole directions, inducing the bipolar outflow of particles from black holes. As a step toward the construction of a non-stationary rotating black hole solution in the presence of matter, we explore the zero angular momentum limit of the constructed metrics. The use of the Eddington-Finkelstein coordinates allows us to find a generalization of the proposed construction to the Vaidya-type black hole. Finally, employing the Newman-Janis algorithm, we find the corresponding generalization of the Kerr-Vaidya black hole solution.