Fixing the BMS frame of numerical relativity waveforms with BMS charges

The Bondi-van der Burg-Metzner-Sachs (BMS) group, which uniquely describes the symmetries of asymptotic infinity and therefore gravitational waves that propagate there, has become increasingly important for accurate modeling waveforms. In particular, waveform models, such as post-Newtonian (PN) expressions, numerical relativity (NR), black hole perturbation theory, produce results are in different BMS frames. Consequently, to build a model waveforms produced during merging compact objects, ideally would be hybridization PN, NR, one needs fast robust method fixing freedoms. this work, we present first means entire freedom NR match frame either PN or theory. We achieve by finding transformations change certain charges prescribed way -- e.g., center-of-mass transformation maps charge mean zero. find new is 20 times faster, more correct when mapping superrest frame, than previous methods relied on optimization algorithms. Furthermore, course developing charge-based method, compute expression Moreschi supermomentum 3PN order without spins 2PN with spins. This effectively equivalent energy flux null memory contribution at future $\mathscr{I}^{+}$. From calculation, also oscillatory ($m\not=0$ modes) spin-dependent terms have not been identified previously missing from strain expressions literature.