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Shear-free or asymptotically shear-free null geodesic congruences possess alarge number of fascinating geometric properties and to be closely related, inthe context of general relativity, to a variety of physically significantaffects. It is the purpose of this paper to develop these issues and findapplications in GR. The applications center around the problem of extractinginterior physical properties of an asymptotically flat space-time directly fromthe asymptotic gravitational (and Maxwell) field itself in analogy with thedetermination of total charge by an integral over the Maxwell field at infinityor the identification of the interior mass (and its loss) by (Bondi's)integrals of the Weyl tensor, also at infinity. More specifically we will seethat the asymptotically shear-free congruences lead us to an asymptoticdefinition of the center-of-mass and its equations of motion. This includes akinematic meaning, in terms of the center of mass motion, for the Bondithree-momentum. In addition, we obtain insights into intrinsic spin and, ingeneral, angular momentum, including an angular momentum conservation law withwell-defined flux terms. When a Maxwell field is present the asymptoticallyshear-free congruences allow us to determine/define at infinity acenter-of-charge world-line and intrinsic magnetic dipole moment.

Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation