Integral Equation for the Spinor Amplitude of a Dirac Particle in a Curved Space-Time

We obtain a system of integral equations for the spinor amplitude of a wave packet describing a massive neutral Dirac particle in a curved space-time with an arbitrary geometry. This equation permits describing the spin dynamics of fermions in gravitational fields adequately to the quantum nature of spin. We consider a specific example of the Kerr–Schild metric. We also discuss the problem of massive neutrino oscillations in an external gravitational field.