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

We derive the new quasi-classical equation for the description of the spin evolution of a neutrino propagating in a curved space-time and interacting with a background matter and an external electromagnetic field. This equation is used to analyze neutrino spin oscillations in these external backgrounds. We obtain the effective Hamiltonian and the transition probability for oscillations of neutrinos when they move in the vicinity of a rotating black hole, surrounded by an accretion disk, and interact with an external magnetic field. The appearance of new resonances in neutrino spin oscillations in this system is considered. The approximate treatment of spin oscillations of radially propagating ultra high energy neutrinos is developed. We also discuss the applications of our results to the description of neutrino spin oscillations in realistic astrophysical media.