  The purpose of this work is to return, with a new observation and rather
unconventional point of view, to the study of asymptotically flat solutions of
Einstein equations. The essential observation is that from a given
asymptotically flat space-time with a given Bondi shear, one can find (by
integrating a partial differential equation) a class of asymptotically
shear-free (but, in general, twistiing) null geodesic congruences. The class is
uniquely given up to the arbitrary choice of a complex analytic world-line in a
four-parameter complex space. Surprisingly this parameter space turns out to be
the H-space that is associated with the real physical space-time under
consideration. The main development in this work is the demonstration of how
this complex world-line can be made both unique and also given a physical
meaning. More specifically by forcing or requiring a certain term in the
asymptotic Weyl tensor to vanish, the world-line is uniquely determined and
becomes (by several arguments) identified as the `complex center-of-mass'.
Roughly, its imaginary part becomes identified with the intrinsic spin-angular
momentum while the real part yields the orbital angular momentum.
