Integrability of Particle Motion and Scalar Field Propagation in Kerr-(Anti) de Sitter Black Hole Spacetimes in All Dimensions

TL;DR

This paper demonstrates the complete integrability of particle motion and scalar field equations in higher-dimensional Kerr-(Anti) de Sitter black hole spacetimes, revealing new symmetries and separation techniques.

Contribution

It generalizes previous results by explicitly constructing Killing tensors and analyzing symmetries for all dimensions with equal rotation parameters.

Findings

Separation of Hamilton-Jacobi and Klein-Gordon equations achieved

Construction of a nontrivial Killing tensor for these backgrounds

Derived first-order equations of motion for particles

Abstract

We study the Hamilton-Jacobi and massive Klein-Gordon equations in the general Kerr-(Anti) de Sitter black hole background in all dimensions. Complete separation of both equations is carried out in cases when there are two sets of equal black hole rotation parameters. We analyze explicitly the symmetry properties of these backgrounds that allow for this Liouville integrability and construct a nontrivial irreducible Killing tensor associated with the enlarged symmetry group which permits separation. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties. This work greatly generalizes previously known results for both the Myers-Perry metrics, and the Kerr-(Anti) de Sitter metrics in higher dimensions.