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- W2007647565 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 ${ensuremath{epsilon}}^{2}$, velocity as ensuremath{epsilon}, pressure as ${ensuremath{epsilon}}^{4}$, where ensuremath{epsilon} is the sequence parameter. We asymptotically approximate the metric at an event which, as ensuremath{epsilon}ensuremath{rightarrow}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 ensuremath{epsilon}ensuremath{rightarrow}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 ${mathit{I}}_{mathrm{FM}}^{+}$. This proves that the quadrupole formula is an asymptotic approximation to general relativity. We study the relation between ${mathit{I}}_{mathrm{ensuremath{epsilon}}}^{+}$, the sequence of null infinities of the individual manifolds, and ${mathit{I}}_{mathrm{FM}}^{+}$; 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." @default.
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- W2007647565 title "Gravitational radiation and the validity of the far-zone quadrupole formula in the Newtonian limit of general relativity" @default.
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- W2007647565 doi "https://doi.org/10.1103/physrevd.32.2557" @default.
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