  We show that certain structures defined on the complex four dimensional space
known as H-Space have considerable relevance for its closely associated
asymptotically flat real physical space-time. More specifically for every
complex analytic curve on the H-space there is an asymptotically shear-free
null geodesic congruence in the physical space-time. There are specific
geometric structures that allow this world-line to be chosen in a unique
canonical fashion giving it physical meaning and significance.
