An equation satisfied by the tangent to a shear-free, geodesic, null congruence
The author presents a tensor equation which is satisfied by the tangent vector of a shear-free null geodesic congruence in general relativity. If the congruence is neither twist-free nor expansion-free, it is shown that this equation defines a second unique null direction. The consequences of this result are discussed and shown to be related to questions involving the construction of exact solutions of the Einstein equations.
scientific article; zbMATH DE number 4011360