Gravitational Aharonov-Bohm effect

We investigate the gravitational Aharonov-Bohm effect, by placing a quantum system in free-fall around a gravitating body {\it e.g.} a satellite orbiting the Earth. Since the system is in free-fall, by the equivalence principle, the quantum system is locally in flat, gravity-free space-time - it is screened from the gravitational field. For a slightly elliptical orbit, the gravitational potential will change with time. This leads to the energy levels of the quantum system developing side bands which is the signature for this version of the Aharonov-Bohm effect. This contrasts with the normal signature of the Aharonov-Bohm effect of shifting of interference fringes.