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

TL;DR

The paper addresses the separability of the Hamilton-Jacobi and Klein-Gordon equations in higher-dimensional Myers-Perry black holes, demonstrating complete separability when there are two sets of equal rotation parameters $a$ and $b$. By exploiting an enlarged dynamical symmetry, it constructs a nontrivial irreducible Killing tensor $K^{\mu\nu}$ and identifies Killing vectors that enable separation of the radial and angular sectors. It then derives explicit first-order equations of motion for particles and provides detailed radial and angular analyses, including turning points and constant-angle trajectories, before extending the separability to the Klein-Gordon equation with separation constants $K$, $K_1$, and $M_1$. These results yield a robust framework for numerical studies of particle motion and scalar field propagation in higher-dimensional rotating black hole spacetimes, with implications for string/M-theory contexts where extra dimensions are essential.

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.