# 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.

## Key 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.