Twistor geometry of light rays

Abstract

The geometry of real and complex light rays (mainly in Minkowski space) is studied using twistor methods. The properties of weak and strong incidence between rays are examined, some apparent anomalies arising for neighbouring rays being explained. Various apparently different interpretations of a complex surface in projective twistor space are given (one coming from the Kerr theorem describing shear-free congruences in Minkowski space). The relations between them are analysed in terms of the caustics of shear-free congruences, null hypersurfaces and a twistor description of spacelike or timelike 2-surfaces. The situation for curved spacetime is also considered. The relation between ray geometry in Minkowski space and a 6-quadric of signature (++++----), with its triality properties, is explored.