Seminarium Teorii Względności i Grawitacji

On a conformal Lorentzian 4-manifold, there are certain foliations of nullgeodesics, known as shearfree congruences of null geodesics (SCNG), which are of central importance in the study of solutions of Einstein's equations. It is well-known that their generators must be principal null directions of the Weyl tensor. What is more, their leaf space is endowed with the structure of a CR manifold.In this talk I will give the integrability condition for the existence of SCNGs in dimension greater than four, and show that remarkably, in even dimension, the connection between SCNGs and (almost) CR structures still subsist under relatively mild curvature conditions on the Weyl tensor.Finally, one can play a similar game in split signature: under suitable curvature prescriptions, SCNGs induce Lagrange contact structures and projective structures.