Transformations of asymptotic gravitational-wave data

TL;DR

This paper develops a method to analyze and mitigate gauge-dependent effects in gravitational-wave data caused by BMS transformations, improving waveform accuracy for numerical and analytical models.

Contribution

It introduces a practical approach to calculate BMS transformations on waveforms, addressing gauge ambiguities and providing open-source tools for waveform correction.

Findings

BMS transformations cause mode-mixing at about 1% level in simulated waveforms.

Measuring and correcting for center of mass motion reduces unmodeled effects.

Controlling BMS transformations is essential for accurate gravitational-wave data analysis.

Abstract

Gravitational-wave data is gauge dependent. While we can restrict the class of gauges in which such data may be expressed, there will still be an infinite-dimensional group of transformations allowed while remaining in this class, and almost as many different---though physically equivalent---waveforms as there are transformations. This paper presents a method for calculating the effects of the most important transformation group, the Bondi-Metzner-Sachs (BMS) group, consisting of rotations, boosts, and supertranslations (which include time and space translations as special cases). To a reasonable approximation, these transformations result in simple coupling between the modes in a spin-weighted spherical-harmonic decomposition of the waveform. It is shown that waveforms from simulated compact binaries in the publicly available SXS waveform catalog contain unmodeled effects due to displacement and drift of the center of mass, accounting for mode-mixing at typical levels of 1%. However, these effects can be mitigated by measuring the average motion of the system's center of mass for a portion of the inspiral, and applying the opposite transformation to the waveform data. More generally, controlling the BMS transformations will be necessary to eliminate the gauge ambiguity inherent in gravitational-wave data for both numerical and analytical waveforms. Open-source code implementing BMS transformations of waveforms is included along with this paper in the supplemental materials.