The generalized Taub-NUT congruence in Minkowski spaces

Abstract

With any shear-free congruence of null geodesics in a Lorentzian geometry there is associated a Cauchy-Riemann three-space; and in certain spacetimes including the Ricci-flat spacetimes with expanding null shear-free (n.s.f.) congruences the deviation form of the congruence picks out an integrable distribution of complex two-spaces in the CR geometry. Conversely, given a CR geometry with an integrable distribution of two-spaces one can construct an associated family of spacetimes with a null, shear-free congruence. The interesting problem is the restrictionRab=0. We consider the case of n.s.f. congruences in Minkowski spacetime constructed from CR geometries of maximal symmetry. The special two-spaces are here taken to be those associated with either the Taub-NUT geometry or, as a limiting case, those associated with the Hauser twisting typeN solution. We obtain the most general solution for these cases.