Particle and light motion in a space-time of a five-dimensional rotating black hole

TL;DR

This paper investigates the trajectories of particles and light around a five-dimensional rotating black hole, revealing the existence of a Killing tensor and the absence of stable equatorial circular orbits.

Contribution

It demonstrates the presence of a Killing tensor in the Myers-Perry metric and derives separable equations of motion for particles and light in five dimensions.

Findings

Existence of a Killing tensor in the Myers-Perry metric

Separable Hamilton-Jacobi equations for particle and light motion

No stable circular orbits in equatorial planes

Abstract

We study motion of particles and light in a space-time of a 5-dimensional rotating black hole. We demonstrate that the Myers-Perry metric describing such a black hole in addition to three Killing vectors possesses also a Killing tensor. As a result, the Hamilton-Jacobi equations of motion allow a separation of variables. Using first integrals we present the equations of motion in the first-order form. We describe different types of motion of particles and light and study some interesting special cases. We proved that there are no stable circular orbits in equatorial planes in the background of this metric.