Embedded Diagrams of Kerr and Non-Kerr black Holes

TL;DR

This paper uses embedded diagrams to compare Kerr and non-Kerr black holes, analyzing how deformation parameters affect their horizons and singularities in the parameter space.

Contribution

It introduces a detailed comparison of Kerr and non-Kerr black holes using embedded diagrams, highlighting the effects of deformation parameters on their properties.

Findings

Embedded diagrams reveal differences in horizon structures.

Deformation parameter $\epsilon$ influences black hole shape.

Non-Kerr black holes can exhibit naked singularities.

Abstract

Embedded diagrams are drawn for investigating the black hole of Kerr and non-Kerr metric. Kerr black holes are characterized by masses $M$ and spin parameters $a$. Non-Kerr black holes also are characterized by the deformation parameters $\epsilon$, which is related to shape of the black hole, in addition to their masses and spins. In this paper, we investigate the behavior of non-Kerr black holes compared with Kerr black holes in the parameter space of ($a$,$\epsilon$) using embedded diagrams. The event horizons and the naked singularity of non-Kerr BHs are discussed in detail.