Gravitational scattering of spinning neutrinos by a rotating black hole with a slim magnetized accretion disk

We study neutrinos gravitationally scattered off a rotating supermassive black hole which is surrounded by a thin accretion disk with a realistic magnetic field. Neutrinos are supposed to be Dirac particles having a nonzero magnetic moment. Neutrinos move along arbitrary trajectories, with the incoming flux being parallel to the equatorial plane. We exactly account for the influence of both gravity and the magnetic field on the neutrino motion and its spin evolution. The general statement that the helicity of an ultrarelativistic neutrino is constant in the particle scattering in an arbitrary gravitational field is proven within the quasiclassical approach. We find the measurable fluxes of outgoing neutrinos taking into account the neutrino spin precession in the external field in curved spacetime. These fluxes turn out to be significantly suppressed for some parameters of the system. Finally, we discuss the possibility to observe the predicted phenomena for core-collapsing supernova neutrinos in our Galaxy.