Gravitoelectromagnetic approach to the gravitational Faraday rotation in stationary spacetimes

Using the $1+3$ formulation of stationary spacetimes we show, in the context of gravitoelectromagnetism, that the plane of the polarization of light rays passing close to a black hole undergoes a rotation. We show that this rotation has the same integral form as the usual Faraday effect; i.e., it is proportional to the integral of the component of the gravitomagnetic field along the propagation path. We apply this integral formula to calculate the Faraday rotation induced by the Kerr and NUT spaces using the quasi-Maxwell form of the vacuum Einstein equations.