The theory of H-space (Q1059881)

The theory of H-space, the four-dimensional manifold of those complex null hypersurfaces of an asymptotically flat space-time which are asymptotically shear-free, is reviewed. In addition to a discussion of the origins of the theory, we present two independent formalisms for the derivation of the basic properties of H-space: that it is endowed with a natural holomorphic complex Riemannian metric which satisfies the vacuum Einstein equations and the Weyl tensor of which is self-dual. We show the connection of our work on H-space to that of Plebanski and to the theory of deformed twistor spaces, due to Penrose. Finally, there is a discussion of the equations of motion in H-space.