A Newman-Penrose Type Formalism for Space-Times with Torsion. Part 3: Neutrino Fields in Einstein-Cartan Theory

摘要

The spin-coefficient formalism is applied to classical neutrino fields in Einstein-Cartan theory. It is shown that the neutrino current vector is tangent to an expansion-free null geodesic congruence with constant and equal twist and shear, which vanish if and only if the congruence is a repeated principal null congruence of the gravitational field. All exact solutions for the case of pure radiation fields are obtained, and it is shown that the only possible ghost solutions have a plane wave metric.