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Title: Gravitational radiation and the validity of the far-zone quadrupole formula in the Newtonian limit of general relativity

Abstract

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/sup 2/, velocity as epsilon, pressure as epsilon/sup 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/sup +//sub F//sub M/. This proves that the quadrupole formula is an asymptotic approximation to general relativity. We study the relation between I/sup +//sub epsilon/, the sequence of null infinities of the individual manifolds, and I/sup +//submore » F//sub M/; 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.« less

Authors:
;
Publication Date:
Research Org.:
Department of Applied Mathematics and Astronomy, University College, Cardiff, P.O. Box 78, Cardiff, United Kingdom and Max-Planck Institut fuer Physik und Astrophyisk, Karl-Schwarzschild Strasse 1, D-8046 Garching bei Muenchen, West Germany
OSTI Identifier:
6384080
Resource Type:
Journal Article
Journal Name:
Phys. Rev. D; (United States)
Additional Journal Information:
Journal Volume: 32:10
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GRAVITATIONAL RADIATION; SPACE-TIME; GRAVITATIONAL FIELDS; METRICS; PERTURBATION THEORY; QUADRUPOLES; TENSORS; MULTIPOLES; RADIATIONS; 657003* - Theoretical & Mathematical Physics- Relativity & Gravitation

Citation Formats

Futamase, T, and Schutz, B F. Gravitational radiation and the validity of the far-zone quadrupole formula in the Newtonian limit of general relativity. United States: N. p., 1985. Web. doi:10.1103/PhysRevD.32.2557.
Futamase, T, & Schutz, B F. Gravitational radiation and the validity of the far-zone quadrupole formula in the Newtonian limit of general relativity. United States. https://doi.org/10.1103/PhysRevD.32.2557
Futamase, T, and Schutz, B F. 1985. "Gravitational radiation and the validity of the far-zone quadrupole formula in the Newtonian limit of general relativity". United States. https://doi.org/10.1103/PhysRevD.32.2557.
@article{osti_6384080,
title = {Gravitational radiation and the validity of the far-zone quadrupole formula in the Newtonian limit of general relativity},
author = {Futamase, T and Schutz, B F},
abstractNote = {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/sup 2/, velocity as epsilon, pressure as epsilon/sup 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/sup +//sub F//sub M/. This proves that the quadrupole formula is an asymptotic approximation to general relativity. We study the relation between I/sup +//sub epsilon/, the sequence of null infinities of the individual manifolds, and I/sup +//sub F//sub M/; 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.},
doi = {10.1103/PhysRevD.32.2557},
url = {https://www.osti.gov/biblio/6384080}, journal = {Phys. Rev. D; (United States)},
number = ,
volume = 32:10,
place = {United States},
year = {Fri Nov 15 00:00:00 EST 1985},
month = {Fri Nov 15 00:00:00 EST 1985}
}