On Kerr black hole deformations admitting a Carter constant and an invariant criterion for the separability of the wave equation

TL;DR

This paper identifies a necessary and sufficient condition for a family of Kerr black hole deformations, which admit a Carter constant, to have separable Klein-Gordon equations, enhancing understanding of wave behavior in these spacetimes.

Contribution

It provides a clear invariant criterion for the separability of the wave equation in Kerr deformations admitting a Carter constant, building on previous work on their general family.

Findings

Derived a necessary and sufficient condition for separability

Established an invariant criterion for wave equation separability

Clarified the structure of Kerr deformations with Carter constants

Abstract

In a previous work of ours, the most general family of Kerr deformations -- admitting a Carter constant -- has been presented. This time a simple, necessary and sufficient condition in order for the aforementioned family to have a separable Klein-Gordon equations is exhibited.