Gravitational analogue of the Aharonov-Casher effect

The gravitational interaction between a massive particle and a spinning particle in the weak-field limit is studied. We show that a system of a spinning pointlike particle and a massive rod exhibit a topological effect analogous to the electromagnetic Aharonov-Casher effect. We discuss the effect also for systems with a cosmic string instead of a massive rod and in the context of (2+1)-dimensional gravity.