Geometric phase in Taub-NUT spacetime

TL;DR

This paper investigates the geometric phase phenomena, including the gravitational Aharonov-Bohm and Pancharatnam-Berry phases, in various stationary and static spacetimes like Taub-NUT, Schwarzschild, and Kerr, highlighting their physical implications.

Contribution

It demonstrates the presence of both geometric phases in stationary spacetimes and only the Pancharatnam-Berry phase in static spacetimes, providing new insights into gravitational phase effects.

Findings

Both Aharonov-Bohm and Pancharatnam-Berry phases occur in stationary spacetimes.

Only the Pancharatnam-Berry phase appears in static spacetimes.

Potential measurements of these phases for primordial black holes are proposed.

Abstract

Constructing the Hamiltonian in the $\eta$-representation, we explore the geometric phase in the Taub-NUT spacetime, which is spherically symmetric and stationary. The geometric phase around a non-rotating Taub-NUT spacetime reveals both the gravitational analog of Aharonov-Bohm effect and Pancharatnam-Berry phase, similar to the rotating Kerr background. On the other hand, only the latter emerges in the spherically symmetric Schwarzschild geometry as well as in the axisymmetric magnetized Schwarzschild geometry. With this result, we argue that the Aharonov-Bohm effect and Pancharatnam-Berry phase both can emerge in the stationary spacetime, whereas only the latter emerges in the static spacetime. We outline plausible measurements of these effects/phases, mostly for primordial black holes.