Measuring multipole moments of Weyl metrics by means of gyroscopes

TL;DR

This paper develops a method to measure the multipole moments of Weyl metrics by analyzing gyroscopic precession, linking theoretical gravitational source properties to observable quantities.

Contribution

It introduces a technique to connect the multipole moments of Weyl metrics with gyroscopic precession measurements, extending to stationary space-times.

Findings

Derived expressions for gyroscopic precession in Weyl metrics

Linked multipole moments to observable precession effects

Extended analysis to gamma-metric and stationary space-times

Abstract

Using the technique of Rindler and Perlick we calculate the total precession per revolution of a gyroscope circumventing the source of Weyl metrics. We establish thereby a link between the multipole moments of the source and an ``observable'' quantity. Special attention deserves the case of the gamma-metric. As an extension of this result we also present the corresponding expressions for some stationary space-times.