Geometric Properties of Neutrino Fields in Curved Space-Time

Abstract

Classical neutrino fields in curved space-time are studied subject to the condition that the neutrino energy tensor Tab satisfies Tabuaub ≠ 0 for all timelike vectors ua. It is shown that the principal null congruence of these neutrino fields is geodesic and that its shear and twist are restricted. In addition, there exists a canonical null tetrad with respect to which Tab assumes a simple form. These conditions, in fact, characterize this class of neutrino fields. In addition, it is shown that if Tab satisfies the stronger condition that Tabub be a timelike or null vector for all timelike vectors ua, then the principal null congruence is also shear-free. Comparisons are made with the well-known properties of the electromagnetic energy tensor.