Geometry of flat-space null geodesic congruences (Q2226049)

The author studies the general explicit generic expression for null geodesic congruences. From each congruence the construction of a virtually unique form of the flat Lorentzian metric that is associated with the congruence is established. Also, the optical parameters for each congruence are calculated, and the important cases of the shear-free congruences are described in detail by the author. The obtained results are related to the asymptotically shear-free null geodesic congruences of asymptotically flat spacetimes and their physical implications.