Gravitational geometric phase

TL;DR

This paper demonstrates that spinors in curved spacetime acquire a geometric phase analogous to the Berry phase, influenced by spacetime curvature, with potential observable effects near black holes and primordial black holes.

Contribution

It introduces the concept of a gravitational geometric phase for spinors, extending Berry phase ideas to curved spacetime, highlighting differences between rotating and static black hole backgrounds.

Findings

Spinors gain a gravitational Berry phase in curved spacetime.

Rotating black holes induce both Aharonov-Bohm and Berry effects.

Static spacetimes induce only the Berry phase.

Abstract

We show that spinors propagating in curved gravitational background acquire an interaction with spacetime curvature, which leads to a quantum mechanical geometric effect. This is similar to what happens in the case of magnetic fields, known as Pancharatnam-Berry phase. As the magnetic and gravitational fields have certain similar properties, e.g. both contribute to curvature, this result is not difficult to understand. Interestingly, while spacetime around a rotating black hole offers Aharonov-Bohm and Pancharatnam-Berry both kinds of geometric effect, a static spacetime offers only the latter. In the bath of primordial black holes, such gravity induced effects could easily be measured due to their smaller radius.