Spin effects in neutrino gravitational scattering

We study spin oscillations of neutrinos gravitationally scattered off a nonrotating black hole (BH). We derive the transition and survival probabilities of spin oscillations in quadratures when neutrinos interacts with BH only. The dependence of the probabilities on the impact parameter is analyzed. Then, we obtain the effective Schr\"{o}dinger equation for neutrino spin oscillations in neutrino scattering off BH surrounded by background matter. This equation is solved numerically in the case of a supermassive BH with a realistic accretion disk. We find that the observed neutrino fluxes can be reduced almost 20% because of spin oscillations when neutrinos experience gravitational scattering. The neutrino interaction with an accretion disk results in the additional asymmetry in the intensities of outgoing fluxes depending on the neutrino trajectory.