


ID:
60307.0,
MPI für Gravitationsphysik / Astrophysical Relativity 
Gravitational radiation and the validity of the farzone quadrupole formula in the Newtonian limit of general relativity 
Authors:  Futamase, Toshifumi; Schutz, Bernard F.  Language:  English  Date of Publication (YYYYMMDD):  19851115  Title of Journal:  Physicsl Review D  Volume:  32  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 nearzone 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 farzone 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 farzone quadrupole formula (the LandauLifshitz formula), as measured both by the Isaacson average stressenergy 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 gaugeinvariance of FM under certain gauge transformations. We also discuss the relation of this calculation with similar ones in the framework of matched asymptotic expansions and others based on the characteristic initialvalue 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 MaxPlanck Institut
für Physik und Astrophyisk, Garching bei München, Germany
and Department of Applied Mathematics and Astronomy, University College, Cardiff

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