Dirac equation in curved spacetime with the metric in the Kerr-Schield form

The solution of the Dirac equation in the wave package form in a slightly curved spacetime (compared with the size of the wave package) was studied. For the metric in the Kerr-Schield form, a system of common differential equations describing spin conditions of massive neutral Dirac particles (neutrinos) was obtained. The effect of depolarization of the massive neutrinos in a gravitational field are discussed. This effect allows a considerable similarity between the theoretical and observed solar neutrino flows to be established if mve ≥ 10-4 eV