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We derive the new quasi-classical equation for the description of the spinevolution of a neutrino propagating in a curved space-time and interacting witha background matter and an external electromagnetic field. This equation isused to analyze neutrino spin oscillations in these external backgrounds. Weobtain the effective Hamiltonian and the transition probability foroscillations of neutrinos when they move in the vicinity of a rotating blackhole, surrounded by an accretion disk, and interact with an external magneticfield. The appearance of new resonances in neutrino spin oscillations in thissystem is considered. The approximate treatment of spin oscillations ofradially propagating ultra high energy neutrinos is developed. We also discussthe applications of our results to the description of neutrino spinoscillations in realistic astrophysical media.

Neutrino spin oscillations in matter under the influence of gravitational and electromagnetic fields