The Asymptotic Falloff of Local Waveform Measurements in Numerical Relativity

Abstract

We examine current numerical relativity computations of gravitational waves, which typically determine the asymptotic waves at infinity by extrapolation from finite (small) radii. Using simulations of a black hole binary with accurate wave extraction at $r=1000M$, we show that extrapolations from the near-zone are self-consistent in approximating measurements at this radius, although with a somewhat reduced accuracy. We verify that $\ddot{I}{ˆ}_4$ is the dominant asymptotic contribution to the gravitational energy (as required by the peeling theorem) but point out that gauge effects may complicate the interpretation of the other Weyl components.