The gravitational Faraday and its dual spin-Hall effects of light arise in space-times of nonzero angular momentum. These effects were studied in stationary, asymptotically flat space-times. Here we study these effects in arbitrary, nonstationary, asymptotically flat space-times. These effects arise from the interaction between light polarization and space-time angular momentum. As a result of such interaction, the phase velocity of left- and right-handed circularly polarized light becomes different, that results in the gravitational Faraday effect. This difference implies different dynamics of these components, that begin to propagate along different paths—the gravitational spin-Hall effect of light. Due to this effect, the gravitational field splits a multicomponent beam of unpolarized light and produces polarized gravitational rainbow. The component separation is an accumulative effect observed in long range asymptotics. To study this effect, we construct uniform eikonal expansion and derive dynamical equation describing this effect. To analyze the dynamical equation, we present it in the local space and time decomposition form. The spatial part of the equation presented in the related optical metric is analogous to the dynamical equation of a charged particle moving in magnetic field under the influence of the Coriolis force.