The generalized Taub-NUT congruence in Minkowski spaces

Details The generalized Taub-NUT congruence in Minkowski spaces The generalized Taub-NUT congruence in Minkowski spaces

Mar 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993gregr..25..225r&link_type=abstract

General Relativity and Gravitation, Volume 25, Issue 3, pp.225-244

Computer Science

Scientific paper

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 restrictionR ab =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.

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