Abstract
The spin-coefficient formalism presented elsewhere is here 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. The geodesics are both extremals and autoparallels. 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.
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Griffiths, J.B. Neutrino fields in Einstein-Cartan theory. Gen Relat Gravit 13, 227–237 (1981). https://doi.org/10.1007/BF00758550
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DOI: https://doi.org/10.1007/BF00758550