Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity

TL;DR

This paper presents a detailed application of the Cauchy-characteristic extraction method in numerical relativity to accurately compute gravitational waveforms at null infinity for binary black hole mergers, reducing systematic errors.

Contribution

It introduces and validates a gauge-invariant wave-extraction technique at null infinity, improving accuracy over traditional finite-radius extrapolation methods.

Findings

Energy and angular momentum conserved with high precision.

Waveforms at null infinity match extrapolated data closely.

Systematic differences are comparable to discretization errors.

Abstract

The accurate modeling of gravitational radiation is a key issue for gravitational wave astronomy. As simulation codes reach higher accuracy, systematic errors inherent in current numerical relativity wave-extraction methods become evident, and may lead to a wrong astrophysical interpretation of the data. In this paper, we give a detailed description of the Cauchy-characteristic extraction technique applied to binary black hole inspiral and merger evolutions to obtain gravitational waveforms that are defined unambiguously, that is, at future null infinity. By this method we remove finite-radius approximations and the need to extrapolate data from the near zone. Further, we demonstrate that the method is free of gauge effects and thus is affected only by numerical error. Various consistency checks reveal that energy and angular momentum are conserved to high precision and agree very well with extrapolated data. In addition, we revisit the computation of the gravitational recoil and find that finite radius extrapolation very well approximates the result at $\scri$. However, the (non-convergent) systematic differences to extrapolated data are of the same order of magnitude as the (convergent) discretisation error of the Cauchy evolution hence highlighting the need for correct wave-extraction.