The two-component neutrino field in general relativity

Abstract

The spinor equations for two-component neutrinos in Riemannian space-time are shown to be equivalent to tensor equations analogous to those for an electromagnetic field with a complex current density vector. The structure of the energy-momentum tensor for neutrinos is more complicated than for the Maxwell field, and in constructing exact solutions of the combined neutrino-gravitational equations it has been found necessary to build up the energy-momentum tensor directly from spinor quantities. Exact solutions for pure radiation fields are obtained in the case of conformally flat and cylindrically symmetric space-times, and also for a non-diagonal radiation metric. It is shown that there are no spherically symmetric radiation solutions for the type of neutrino field considered.