Geometric Aharonov-Bohm phase effect around a black hole

Abstract

In recent work, we have explored the novel possibility that the geodesic of a spacetime density flow in GR could be upgraded to an amplitude $ψ$ with density $|ψ|^2$. We show how this arises from generally-covariant quantum mechanics and the Klein-Gordon operator in a semiclassical analysis, and how it connects to the Raychaudhuri equations. In this setting, we demonstrate an Aharonov-Bohm type effect for the phase of $ψ$ in motion approaching a black hole.