Geodesic
Massive neutral Dirac particle in a curved space--time with the Kerr--Schild metric
Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 2, pp. 343-352

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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. 
@article{TMF_2000_125_2_a11,
     author = {D. E. Kumpyak and V. P. Tsvetkov},
     title = {Massive neutral {Dirac} particle in a curved space--time with the {Kerr--Schild} metric},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {343--352},
     publisher = {mathdoc},
     volume = {125},
     number = {2},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_125_2_a11/}
}
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D. E. Kumpyak; V. P. Tsvetkov. Massive neutral Dirac particle in a curved space--time with the Kerr--Schild metric. Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 2, pp. 343-352. http://geodesic.mathdoc.fr/item/TMF_2000_125_2_a11/