Separability and Hidden Symmetries of Kerr-Taub-NUT Spacetime in Kaluza-Klein Theory

TL;DR

This paper investigates the separability and hidden symmetries of Kerr-Taub-NUT spacetime within Kaluza-Klein theory, revealing that only massless geodesics allow complete separation and identifying the associated conformal Killing tensor.

Contribution

It demonstrates the conditions for separability of the Hamilton-Jacobi equation and explicitly constructs the conformal Killing tensor in Kerr-Taub-NUT spacetime in Kaluza-Klein theory.

Findings

Complete separation of variables for massless geodesics

Existence of hidden symmetries via conformal Killing tensor

Explicit expression for the conformal Killing tensor

Abstract

The Kerr-Taub-NUT spacetime in the Kaluza-Klein theory represents a localized stationary and axisymmetric object in four dimensions from the Kaluza-Klein viewpoint. That is, it harbors companion electromagnetic and dilaton fields, thereby showing up the signature of the extra fifth dimension. We explore the separability structure of this spacetime and show that the Hamilton-Jacobi equation for geodesics admits the complete separation of variables only for massless geodesics. This implies the existence of the hidden symmetries in the spacetime, which are generated by the conformal Killing tensor. Using a simple trick built up on a conformally related metric (an "effective" metric) with the Killing tensor, we construct the explicit expression for the conformal Killing tensor.