Gaussian Curvature and Global effects : gravitational Aharonov-Bohm effect revisited

TL;DR

This paper revisits the gravitational Aharonov-Bohm effect using the Gauss-Bonnet formula within the full Einstein equations, revealing additional classical effects in stationary spacetimes beyond previous linearized results.

Contribution

It extends prior linearized analyses by applying the 1+3 spacetime decomposition to full Einstein equations, uncovering new classical effects in stationary gravitational configurations.

Findings

Recovered previous results for dust distributions

Identified an extra term representing the COW effect

Demonstrated the approach in static tube-like and cylindrical spacetimes

Abstract

Using the Gauss-Bonnet formula, integral of the Gaussian curvature over a 2-surface enclosed by a curve in the asymptotically flat region of a static spacetime was found to be a measure of a gravitational analogue of Aharonov-Bohm effect by Ford and Vilenkin in the linearized regime. Employing the 1+3 formulation of spacetime decomposition we study the same effect in the context of full Einstein field equations for stationary spacetimes. Applying our approach to static tube-like and cylindrical distributions of dust not only we recover their result but also obtain an extra term which is interpreted to be representing the classical version of the Colella-Overhauser-Werner effect (the COW experiment).