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Twisting Null Geodesic Congruences, Scri, H-Space and Spin-Angular Momentum

Carlos. Kozameh·E. T. Newman·Gilberto Silva-Ortigoza
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Abstract

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.

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Carlos. Kozameh, E. T. Newman, Gilberto Silva-Ortigoza. 2005-06-08. Twisting Null Geodesic Congruences, Scri, H-Space and Spin-Angular Momentum. https://doi.org/10.1088/0264-9381%2F22%2F22%2F003

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