Separability of the Hamilton-Jacobi and Klein-Gordon Equations in Kerr-de Sitter Metrics

TL;DR

This paper investigates the separability of the Hamilton-Jacobi and Klein-Gordon equations in higher-dimensional Kerr-de Sitter spacetimes, revealing conditions for complete separation and constructing associated symmetries.

Contribution

It demonstrates complete separability in all dimensions for equal rotation parameters and constructs new Killing vectors related to the enlarged symmetry group.

Findings

Complete separation achieved in 2n+1 dimensions with equal rotation parameters

Explicit construction of additional Killing vectors

Derived first-order particle equations of motion

Abstract

We study separability of the Hamilton-Jacobi and massive Klein-Gordon equations in the general Kerr-de Sitter spacetime in all dimensions. Complete separation of both equations is carried out in 2n+1 spacetime dimensions with all n rotation parameters equal, in which case the rotational symmetry group is enlarged from (U(1))^n to U(n). We explicitly construct the additional Killing vectors associated with the enlarged symmetry group which permit separation. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties.