Gravito-electromagnetic Effects of Massive Rings

TL;DR

This paper investigates the gravito-electromagnetic effects of a massive, rotating ring using the linear post-Newtonian approximation, extending previous models to include rotation and potential angular momentum inference.

Contribution

It generalizes previous Newtonian models by incorporating gravito-magnetic effects of rotating rings in the gravito-electromagnetic formalism.

Findings

Derived the gravitational field of a rotating massive ring in the gravito-electromagnetic framework.

Analyzed the influence of ring rotation on the gravitational field.

Suggested methods to infer ring angular momentum from gravitational effects.

Abstract

The Einstein field equations in linear post-Newtonian approximation can be written in analogy with electromagnetism, in the so-called gravito-electromagnetic formalism. We use this analogy to study the gravitational field of a massive ring: in particular, we consider a continuous mass distribution on Keplerian orbit around a central body, and we work out the gravitational field generated by this mass distribution in the intermediate zone between the central body and the ring, focusing on the gravito-magnetic component that originates from the rotation of the ring. In doing so, we generalize and complement some previous results that focused on the purely Newtonian effects of the ring (thus neglecting its rotation) or that were applied to the case of rotating spherical shells. Eventually, we study in some simple cases the effect of the the rotation of the ring, and suggest that, in principle, this approach could be used to infer information about the angular momentum of the ring.