  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.
