Abstract
The combined gravitational-neutrino field equations are solved, subject only to the restriction that the energy-flow vector of the neutrino field be timelike or null. The principal null congruence (pnc) of the neutrino field is necessarily geodesic and shear-free, and coincides with a repeated pnc of the gravitational field, which is thus algebraically special. The twist of the neutrino pnc plays an important role, and is zero if and only if the neutrino energy-flow vector is null, in which case the neutrino field represents pure radiation.
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