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Abstract When numerically solving Einstein’s equations for the evolution of binary black holes, physical imperfections in the initial data manifest as a transient, high-frequency pulse of ‘junk radiation.’ This unphysical signal must be removed before the waveform can be used. Improvements in the efficiency of numerical simulations now allow waveform catalogs containing thousands of waveforms to be produced. Thus, an automated procedure for identifying junk radiation is required. To this end, we present a new algorithm based on the empirical mode decomposition (EMD) from the Hilbert–Huang transform. This approach allows us to isolate and measure the high-frequency oscillations present in the measured irreducible masses of the black holes. The decay of these oscillations allows us to estimate the time from which the junk radiation can be ignored. To make this procedure more precise, we propose three distinct threshold criteria that specify how small the contribution of junk radiation has to be before it can be considered negligible. We apply this algorithm to 3403 BBH simulations from the Simulating eXtreme Spacetime catalog to find appropriate values for the thresholds in the three criteria. We find that this approach yields reliable decay time estimates, i.e. when to consider the simulation physical, for $>$98.5% of the simulations studied. This demonstrates the efficacy of the EMD as a suitable tool to automatically isolate and characterize junk radiation in the simulation of binary black hole systems. 

Abstract Gravitational memory effects and the BMS freedoms exhibited at future null infinity have recently been resolved and utilized in numerical relativity simulations. With this, gravitational wave models and our understanding of the fundamental nature of general relativity have been vastly improved. In this paper, we review the history and intuition behind memory effects and BMS symmetries, how they manifest in gravitational waves, and how controlling the infinite number of BMS freedoms of numerical relativity simulations can crucially improve the waveform models that are used by gravitational wave detectors. We reiterate the fact that, with memory effects and BMS symmetries, not only can these next-generation numerical waveforms be used to observe never-before-seen physics, but they can also be used to test GR and learn new astrophysical information about our Universe.