  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).
