Killing tensors of generalized Lense-Thirring space-time

TL;DR

This paper studies the integrability of particle motion in a generalized Lense-Thirring spacetime, revealing it is super-integrable with additional constants of motion and analyzing associated Killing tensors.

Contribution

It demonstrates super-integrability of geodesic motion in the generalized Lense-Thirring spacetime and explores the structure of second rank Killing tensors.

Findings

Motion is super-integrable with extra constants of motion.

Generalized Lense-Thirring differs from Myers-Perry black hole at second order.

Identifies second rank Killing tensors in the spacetime.

Abstract

We investigate the Hamilton-Jacobi equation of a probe particle moving on d-dimensional generalized Lense-Thirring metric. This space-time is different from the slowly rotating Myers-Perry black hole at second order in rotation parameters. We show that the dynamics of the probe particle along the time-like geodesic of the generalized Lense-Thirring space-time is super-integrable and has more constants of motion with respect to the same dynamics on Myers-Perry black hole. We also discuss the second rank Killing tensors associated with the generalized Lense-Thirring metric.