The large footprints of H-space on asymptotically flat spacetimes

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 spacetime. More specifically, for every complex analytic curve on the H-space there is an asymptotically shear-free null geodesic congruence in the physical spacetime. There are specific geometric structures that allow this worldline to be chosen in a unique canonical fashion giving it physical meaning and significance