Gravitational Faraday rotation in a weak gravitational field

We examine the rotation of the plane of polarization for linearly polarized light rays by the weak gravitational field of an isolated physical system. Based on the rotation of inertial frames, we review the general integral expression for the net rotation. We apply this formula, an analogue to the usual electromagnetic Faraday effect, to some interesting astrophysical systems, namely uniformly shifting mass monopoles and a spinning external shell.