  We study the gravitational scattering of ultrarelativistic neutrinos off a
rotating supermassive black hole (BH) surrounded by a thick magnetized
accretion disk. Neutrinos interact electroweakly with background matter and
with the magnetic field in the disk since neutrinos are supposed to possess
nonzero magnetic moments. The interaction with external fields results in
neutrino spin oscillations. We find that the toroidal magnetic field, inherent
in the magnetized Polish doughnut, does not cause a significant spin-flip for
any reasonable strengths of the toroidal component. The reduction of the
observed neutrino flux, owing to neutrino spin oscillations, is predicted. A
poloidal component of the magnetic field gives the main contribution to the
modification of the observed flux. The neutrino interaction with matter,
rotating with relativistic velocities, also changes the flux of neutrinos. We
briefly discuss the idea of the neutrino tomography of magnetic field
distributions in accretion disks near BHs.
