Massive neutral Dirac particle in a curved space-time with the Kerr-Schild metric

A method for constructing the solution of the general covariant Dirac equation is developed. The solution has the form of a wave packet in the case of a slightly (compared to the wave packet size) curved space-time with the Kerr-Schild metric and describes the evolution of the spin states of a massive neutral particle with a half-integer spin. The method allows reducing the Dirac equation to a system of ordinary differential equations for the spinor amplitudes (with the necessary accuracy). We propose an iterative procedure for solving the system based on expansion with respect to a small parameter equal to the ratio between the particle wave length and the characteristic spatial scale of the change of the metric. The characteristic dissipation time of a wave packet moving in a curved space-time is estimated.