Generalized Runge-Lenz Vector in Taub-Nut Spinning Space

TL;DR

This paper explores the symmetries of Taub-NUT spinning space, deriving a generalized Runge-Lenz vector that accounts for spin contributions, extending understanding of conserved quantities in such geometries.

Contribution

It introduces a fully evaluated generalized Runge-Lenz vector for spinning Taub-NUT space, incorporating spin effects into the conserved quantities.

Findings

Runge-Lenz vector for spinless particles is a constant of motion.

Spin contributions modify the form of the Runge-Lenz vector.

Complete evaluation of the generalized Runge-Lenz vector for spinning particles.

Abstract

The generalized Killing equations and the symmetries of Taub-NUT spinning space are investigated. For spinless particles the Runge-Lenz vector defines a constant of motion directly, whereas for spinning particles it now requires a non-trivial contribution from spin. The generalized Runge-Lenz vector for spinning Taub-NUT space is completely evaluated.