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ID: 60307.0, MPI für Gravitationsphysik / Astrophysical Relativity
Gravitational radiation and the validity of the far-zone quadrupole formula in the Newtonian limit of general relativity
Authors:Futamase, Toshifumi; Schutz, Bernard F.
Date of Publication (YYYY-MM-DD):1985-11-15
Title of Journal:Physicsl Review D
Issue / Number:10
Start Page:2557
End Page:2565
Review Status:not specified
Abstract / Description:We examine the gravitational radiation emitted by a sequence of spacetimes whose near-zone Newtonian limit we have previously studied. The spacetimes are defined by initial data which scale in a Newtonian fashion: the density as epsilon 2, velocity as epsilon , pressure as epsilon 4, where epsilon is the sequence parameter. We asymptotically approximate the metric at an event which, as epsilon -->0, remains a fixed number of gravitational wavelengths distant from the system and a fixed number of wave periods to the future of the initial hypersurface. We show that the radiation behaves like that of linearized theory in a Minkowski spacetime, since the mass of the metric vanishes as epsilon -->0. We call this Minkowskian far-zone limiting manifold FM; it is a boundary of the sequence of spacetimes, in which the radiation carries an energy flux given asymptotically by the usual far-zone quadrupole formula (the Landau-Lifshitz formula), as measured both by the Isaacson average stress-energy tensor in FM or by the Bondi flux on I+FM. This proves that the quadrupole formula is an asymptotic approximation to general relativity. We study the relation between I+ epsilon , the sequence of null infinities of the individual manifolds, and I+FM; and we examine the gauge-invariance of FM under certain gauge transformations. We also discuss the relation of this calculation with similar ones in the frame-work of matched asymptotic expansions and others based on the characteristic initial-value problem.
External Publication Status:published
Document Type:Article
Communicated by:Bernhard F. Schutz
Affiliations:MPI für Gravitationsphysik/Astrophysical Relativity
External Affiliations:Department of Applied Mathematics and Astronomy, University College, Cardiff, United Kingdom and Max-Planck Institut
für Physik und Astrophyisk, Garching bei München, Germany
and Department of Applied Mathematics and Astronomy, University College, Cardiff
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