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The Bondi–van der Burg–Metzner–Sachs (BMS) frame of gravitational waves produced by numerical relativity simulations is crucial for building accurate waveform models. A proper comparison of numerical relativity waveforms with other models requires fixing the arbitrary BMS frame. In this work we improve the center-of-mass (c.m.) frame fixing for quasicircular, nonprecessing binary systems. Past work approximated the c.m. motion with just a linear fit. We compute a post-Newtonian result of the boosted c.m. charge to also capture its physical outspiraling oscillations. We show that using the analytical results improves the robustness of the fit parameters—translation and boost vectors—to the choice of duration and time of the fitting window. Our analysis demonstrates a maximum improvement in robustness when the window is placed at the center of the inspiral. We quantified this improvement by computing the ratio of variances of fit parameters when the fit window size is varied. The largest improvement in robustness of parameters is by a factor of ∼25 for the boost vector and ∼20 for the translation vector. Finally, we incorporate this method into the BMS frame-fixing routine of the PYTHON package SCRI for waveforms produced with Cauchy-characteristic evolution. 

Future gravitational wave detections of merging binary neutron star systems have the possibility to tightly constrain the equation of state of dense nuclear matter. In order to extract such constraints, gravitational waveform models need to be calibrated to accurate numerical relativity simulations of the late inspiral and merger. In this work, we take an essential step toward classifying the error and potential systematics in current generation numerical relativity simulations of merging binary neutron stars. To this end, we perform a direct comparison of two codes (FIL, SpEC), which differ in many aspects, including the numerical methods and discretizations used and equations solved. We find that despite these different approaches, the codes are—within current numerical resolution bounds—fully consistent, and broadly comparable in cost for a given accuracy level. Our results indicate that the error in the waveforms is primarily dominated by the hydrodynamic evolution, consistent with earlier findings in the literature. We also discuss current limitations and cost estimates for numerical relativity simulations to reach the accuracies required in the era of next-generation gravitational detectors. 

Abstract Cauchy-characteristic evolution (CCE) is a powerful method for accurately extracting gravitational waves at future null infinity. In this work, we extend the previously implemented CCE system within the numerical relativity code SpECTRE by incorporating a scalar field. This allows the system to capture features of beyond-general-relativity theories. We derive scalar contributions to the equations of motion, Weyl scalar computations, Bianchi identities, and balance laws at future null infinity. Our algorithm, tested across various scenarios, accurately reveals memory effects induced by both scalar and tensor fields and captures Price’s power-law tail ( $u^{-l-2}$) in scalar fields at future null infinity, in contrast to the $t^{-2l-3}$tail at future timelike infinity. 

We uncover late-time gravitational-wave tails in fully nonlinear $3+1$dimensional numerical relativity simulations of merging black holes, using the highly accurate p code. We achieve this result by exploiting the strong magnification of late-time tails due to binary eccentricity, recently observed in perturbative evolutions, and showcase here the tail presence in head-on configurations for several mass ratios close to unity. We validate the result through a large battery of numerical tests and detailed comparison with a perturbative evolution, which display striking agreement with full nonlinear ones in the ringdown regime, and very similar tail morphologies. Our results offer yet another confirmation of the highly predictive power of black hole perturbation theory in the presence of a source, even when applied to nonlinear solutions. The late-time tail signal is much more prominent than anticipated until recently, and possibly within reach of gravitational-wave detector measurements, unlocking observational investigations of an additional set of general relativistic predictions on the long-range gravitational dynamics.