Gravito-electromagnetic effects of massive rings

The Einstein field equations in linear post-Newtonian approximation can be written in analogy with electromagnetism, in the so-called gravito-electromagnetic (GEM) 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 gravitomagnetic (GM) 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 rotation of the ring, and suggest that, in principle, this approach could be used to infer information about the angular momentum of the ring.