Vol. 12 (2009) > lrr-2009-6

doi: 10.12942/lrr-2009-6
Living Rev. Relativity 12 (2009), 6

Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation

1 University of Oxford, Mathematical Institute, 24-29 St Giles, Oxford, OX1 3LB, U.K.
2 Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Argentina
3 Department of Physics and Astronomy, University of Pittsburgh, U.S.A.

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Article Abstract

A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to 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 effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in complex Minkowski space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime 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.

Keywords: H-space, Shear-free congruences, Spin-coefficient formalism, Asymptotic flatness

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Since a Living Reviews in Relativity article may evolve over time, please cite the access <date>, which uniquely identifies the version of the article you are referring to:

Timothy M. Adamo and Carlos Kozameh and Ezra T. Newman,
"Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation",
Living Rev. Relativity 12,  (2009),  6. URL (cited on <date>):

Article History

ORIGINAL http://www.livingreviews.org/lrr-2009-6
Title Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation
Author Timothy M. Adamo / Carlos Kozameh / Ezra T. Newman
Date accepted 5 August 2009, published 11 September 2009
Date accepted 23 June 2010, published 25 June 2010
Changes The two major changes are the addition of Appendix D, and that we have rewritten about a quarter of Section 7. The extra appendix was just to add new information while the changes in Section 7 were due to real errors on our part. In addition there were many very small changes, words changed here and there; a few small paragraphs were added as well. These word changes were needed to correct the errors (mainly language) in Section 7. Several misprints were also corrected and a new reference to Adamo and Newman (2010) was added. For detailed description see here .

RefDB records now cited by this article:
UPDATE http://www.livingreviews.org/lrr-2012-1
Title Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation
Author Timothy M. Adamo / Ezra T. Newman / Carlos Kozameh
Date accepted 16 January 2012, published 23 January 2012
Changes These revisions were done exclusively by Adamo and Newman, therefore the author order was slightly changed. There was nothing essentially wrong in the earlier version, but we have included several new results (in the text and in appendices), corrected an error of interpretation in Section 7, and (the main reason for the revision) we found much easier ways of doing some of the long calculations with very much simpler arguments. 19 new references were added.
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