Gravitational Faraday and spin-Hall effects of light: Local description

A gravitational field can cause a rotation of the polarisation plane of light. This phenomenon is known as the gravitational Faraday effect. It arises due to different spin-orbit interaction of left- and right-handed circularly polarised components of light. Such an interaction also causes transverse displacement in the light trajectory, in opposite directions for each component. This phenomenon is known as the gravitational spin-Hall effect of light. We study these effects in a local inertial frame in arbitrary vacuum space-time and show that they are observer dependent and arise due to interaction of light polarisation with a local gravitomagnetic field measured by observer. Thus, to address the effects to a gravitational field alone, one has to consider zero angular momentum observers.