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

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.

26 pages, authors were relisted alphabetically

References in corpus (4)

• On a Classical, Geometric Origin of Magnetic Moments, Spin-Angular Momentum and the Dirac Gyromagnetic Ratio
• Constraints Algebra and Equations of Motion in Bohmian Interpretation of Quantum Gravity
• The Large Footprints of H-Space on Asymptotically Flat Space-Times
• Electromagnetic Dipole Radiation Fields, Shear-Free Congruences and Complex Center of Charge World Lines

Cited by in corpus (8)

• Tensorial Spin-s Harmonics
• On the Physical Meaning of the Robinson-Trautman-Maxwell Fields
• CR Structures and Asymptotically Flat Space-Times
• The Universal Cut Function and Type II Metrics
• Twisting Null Geodesic Congruences and the Einstein-Maxwell Equations
• Asymptotic twistor Theory and the Kerr Theorem
• The Geometry of Regular Shear-Free Null Geodesic Congruences, CR functions and their Application to the Flat-Space Maxwell Equations
• Angular momentum, spinors and twistors