Gravitational radiation and the validity of the far-zone quadrupole formula in the Newtonian limit of general relativity
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.
- Research Organization:
- 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 ID:
- 6384080
- Journal Information:
- Phys. Rev. D; (United States), Vol. 32:10
- Country of Publication:
- United States
- Language:
- English
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