Geodesic deviation on symmetry axis in Taub-NUT metric

TL;DR

This paper investigates the tidal effects in the axially symmetric Taub-NUT spacetime using the geodesic deviation equation, revealing how NUT-charge influences tidal forces and their behavior across the spacetime.

Contribution

It provides a detailed analysis of tidal forces along radial geodesics in Taub-NUT spacetime, including solutions to the geodesic deviation equation and insights into tidal force behavior near the event horizon.

Findings

Spatial tidal forces change sign at the event horizon.

All tidal force components are regular throughout spacetime.

NUT-charge affects the magnitude of tidal deviations.

Abstract

An important aspect of General Relativity is to study properties of geodesics. A useful tool for describing geodesic behavior is the geodesic deviation equation. It allows to describe the tidal properties of gravitating objects through the curvature of spacetime. This article focuses on the study of the axially symmetric Taub-NUT metric. We study tidal effects in this metric using the geodesic deviation equation. Radial geodesics along the symmetry axis of spacetime are considered. We show that all spatial components of tidal forces always change sign under the event horizon. We find a solution of the geodesic deviation equation for all geodesic deviation vector components. It allows us to quantify the effect of the NUT-charge on the tidal properties of Taub-NUT metric. And another important feature that we found is the regular behavior of all tidal force components at all points of spacetime.