Spin precession in a weak gravitational field

Previously developed technique for calculating spin precession velocity in Schwarzschild field was applied for the case of arbitrary weak gravitational field. The obtained expression for precession velocity in limiting cases (nonrelativistic particle velocity and in post-Newton approximation) coincides with earlier known formulae. If v test particle velocity tends to 1, we obtain the expression for precession velocity of photon polarization vector, which contains the summand describing the rotation of photon polarization plane