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

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

2009-06-11

arxiv.org/abs/0906.2155v3

Living Rev. Relativity,15:1, 2012

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

98 pages, 6 appendices. v2: typos corrected; v3: significant changes made to results section using simpler arguments, added di

Scientific paper

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

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