Particle Motion and Scalar Field Propagation in Myers-Perry Black Hole Spacetimes in All Dimensions

TL;DR

This paper investigates the separability of key equations governing particle motion and scalar fields in Myers-Perry black hole spacetimes across all dimensions, revealing new symmetries and explicit solutions.

Contribution

It demonstrates complete separability of the Hamilton-Jacobi and Klein-Gordon equations in specific symmetric Myers-Perry backgrounds and constructs associated Killing tensors.

Findings

Separation achieved in cases with equal rotation parameters

Explicit construction of a nontrivial Killing tensor

Derived first-order equations of particle motion

Abstract

We study separability of the Hamilton-Jacobi and massive Klein-Gordon equations in the general Myers-Perry 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, which significantly enlarges the rotational symmetry group. We explicitly 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.