Sharpening the gravitational Aharonov–Bohm effect

We study the recent gravitational analogue of the Aharonov–Bohm effect for a classical system, namely a complex scalar field. We use this example to demonstrate that the Aharonov–Bohm effect in principle has nothing to do with quantum-mechanics. We then discuss how this classical field description can be connected to the standard one particle quantum description of the Aharonov–Bohm effect.