The Geodesic Motion on Generalized Taub-Nut Gravitational Instantons

TL;DR

This paper investigates the motion of particles on generalized Taub-NUT gravitational instantons in five-dimensional Einstein gravity, revealing non-conic orbit shapes and introducing a generalized Runge-Lenz vector.

Contribution

It introduces a new class of gravitational instantons and analyzes their geodesic motion, including the derivation of a generalized Runge-Lenz vector, expanding understanding of particle dynamics in these spacetimes.

Findings

Orbits are not conic sections unlike classical Kepler or Taub-NUT cases.

A generalized Runge-Lenz vector is constructed for these instantons.

The study extends the understanding of geodesic motion in higher-dimensional gravitational instantons.

Abstract

A class of generalized Taub-NUT gravitational instantons is reported in five - dimensional Einstein gravity coupled to a non-linear sigma model. The geodesic dynamics of a spinless particle of unit mass on these static gravitational instantons is studied. This is accomplished by finding a generalized Runge-Lenz vector. Unlike the Kepler problem, or, the dynamics of a spinless particle on the familiar Taub-NUT gravitational instantons, the orbits are not conic sections.