Embedded Diagrams of Kerr and Non-Kerr black Holes

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 $ϵ$, 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 ($a$,$ϵ$) using embedded diagrams. The event horizons and the naked singularity of non-Kerr BHs are discussed in detail.