The Asymptotic Falloff of Local Waveform Measurements in Numerical Relativity

TL;DR

This paper investigates the accuracy of gravitational wave measurements in numerical relativity, demonstrating that extrapolation from finite radii can reliably approximate asymptotic waves, with some gauge-related complexities.

Contribution

It provides a detailed analysis of wave extraction methods at finite radii and confirms the dominance of c4 in gravitational energy calculations, highlighting gauge effects.

Findings

Extrapolation from finite radii can accurately approximate asymptotic gravitational waves.

c4 is confirmed as the dominant contribution to gravitational energy.

Gauge effects may influence interpretation of other Weyl components.

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 $\psi_4$ 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.