Testing gravitational waveforms in full General Relativity

We perform a comprehensive analysis of state-of-the-art waveform models, focusing on their predictions concerning kick velocity and inferred gravitational wave memory. Recent advancements in gravitational wave instrumentation have established new benchmarks for the precision of future measurements. To fully exploit the potential of upcoming gravitational wave surveys, it is crucial to concurrently enhance both semi-analytical and numerical waveform models used for analyzing interferometer data. In this work, we establish a pathway towards achieving this goal by developing and implementing a pipeline to assess the accuracy of waveform models using energy-momentum balance laws derived in full, non-linear General Relativity. The numerical accuracy assessment is performed for precessing as well as non-precessing simulations for models belonging to the EOB, Phenom, and Surrogate inaccuracies in modeling subdominant modes and inherent systematic errors in the chosen models. We corroborate our findings through analytical considerations regarding the mixing of harmonic modes in the computed kick velocities and inferred memories. The methodology developed and validated in this article provides a foundational approach for future waveform assessments and a selection guide for waveform models in practical applications.