Constants of Geodesic Motion in Higher-Dimensional Black-Hole Spacetimes

TL;DR

This paper proves the complete integrability of geodesic motion in higher-dimensional rotating black-hole spacetimes by establishing the independence and commutation of constants of motion, confirming earlier conjectures.

Contribution

It provides a rigorous proof of integrability, including independence and Poisson commutation of constants of motion, in higher-dimensional black-hole spacetimes.

Findings

Constants of motion are independent.

Constants of motion Poisson commute.

Complete integrability of geodesic equations established.

Abstract

In [arXiv:hep-th/0611083] we announced the complete integrability of geodesic motion in the general higher-dimensional rotating black-hole spacetimes. In the present paper we prove all the necessary steps leading to this conclusion. In particular, we demonstrate the independence of the constants of motion and the fact that they Poisson commute. The relation to a different set of constants of motion constructed in [arXiv:hep-th/0612029] is also briefly discussed.