Geometry of flat-space null geodesic congruences

Abstract

In Minkowski space-time, (locally) space-filling families of null geodesics i.e., null geodesic congruences, appear in a variety different physical contexts. We here describe what appears to be the general explicit generic expression for these congruences. From each congruence one can construct a (virtually) unique form of the flat Lorentzian metric that is associated with the congruence. In addition, the “so-called” optical parameters for each congruence are calculated. The very important special cases of the shear-free congruences (twisting and non-twisting) are described in detail. These results are closely related to the asymptotically shear-free null geodesic congruences of asymptotically flat space-times and their rather surprising physical implications.