hide
Free keywords:

Abstract:
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 ε2, velocity as ε, pressure as ε4, where ε is the sequence parameter. We asymptotically approximate the metric at an event which, as ε→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 ε→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 IFM+. This proves that the quadrupole formula is an asymptotic approximation to general relativity. We study the relation between Iε+, the sequence of null infinities of the individual manifolds, and IFM+; 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.