Separability of the Klein-Gordon equation for rotating spacetimes obtained from Newman-Janis algorithm

TL;DR

This paper investigates the conditions under which the Klein-Gordon equation can be separated in rotating spacetimes derived from the Newman-Janis algorithm, extending understanding of wave equations in these geometries.

Contribution

It identifies specific conditions for the separability of the Klein-Gordon equation in NJA-generated spacetimes, expanding the theoretical framework for analyzing wave behavior in rotating black hole backgrounds.

Findings

Separable Klein-Gordon equation conditions derived

Relations between NJA spacetimes and other axially symmetric models discussed

Extension of separability results to more general spacetimes

Abstract

In the literature, the Newman-Janis algorithm (NJA) has been widely used to construct stationary and axisymmetric spacetimes to describe rotating black holes. In addition, it has been recently shown that the general stationary and axisymmetric spacetime generated through NJA allows the complete separability of the null geodesic equations. In fact, the Hamilton-Jacobi equation in this spacetime is also separable if one of the metric functions is additively separable. In this work, we further study the conditions for a separable Klein-Gordon equation in such a general spacetime. The relations between the NJA spacetime and other parameterized axially symmetric spacetimes in the literature are also discussed.