  Spin oscillations of neutrinos, gravitationally scattered off a black hole
(BH), are studied. The cases of nonrotating and rotating BHs are analyzed. We
derive the analytic expressions for the transition and survival probabilities
of spin oscillations when neutrinos interact with these gravitational
backgrounds. The obtained transition probabilities depend on the impact
parameter, as well as the neutrino energy and the particle mass. We find that
there is a possibility of spin oscillations of ultrarelativistic neutrinos
scattering off a rotating BH. Then, considering the neutrino scattering off BH
surrounded by background matter, we derive the effective Schrodinger equation
for spin oscillations. The numerical solution of this equation is obtained in
the case of a supermassive BH with a realistic accretion disk. Spin effects
turn out to be negligible in the neutrino scattering in the Schwarzschild
metric. In the Kerr metric, we find that the observed neutrino fluxes can be
reduced almost 10% because of spin oscillations when ultrarelativistic
neutrinos experience gravitational scattering. The neutrino interaction with an
accretion disk results in the additional modification of the intensities of
outgoing neutrino fluxes. We consider the applications of the obtained results
for the neutrino astronomy.
