The Gravitational_redshift shows, that the wavelength of light gets altered in a gravitational field. But what about polarization of light? I imagine that e.g. by tidal forces circular polarized light could get deformed into elliptic polarized light. Is this possible? Or is polarization of light an invariant quantity in a gravitational field?
Fermi transport will be the equations that describe how each polarisation component changes direction, as the ray passes through the gravitational field (or rather, curved spacetime). So for circular polarisation to become eliptical, you need to check whether othogonal components cease to be orthogonal (when Fermi-Walker transported along an arbitrary trajectory). It turns out that inner products are preserved (so the angle of polarisation may be altered depending on the trajectory through space-time, but the ellipticity shouldn't change in vacuum). However, this assumes the short-wavelength (ray-optics) limit, so you might get a more complex answer by considering extremely low frequencies.