Modeling the BMS transformation between the initial and final states of a binary black hole merger

Understanding the characteristics of the remnant black hole produced in a binary black hole merger is crucial for conducting gravitational wave astronomy. Typically, models of these remnant black holes provide information about their mass, spin, and kick velocity. However, other information related to the supertranslation symmetries of the BMS group, such as the memory effect, is also important for characterizing the system's final state. In this work, we present a model for the BMS transformation that maps a binary black hole merger's inspiral frame to the remnant black hole's rest frame. The computations are based on several high-precision numerical relativity simulations of quasi-circular systems with mass ratios q ≤ 8 and aligned spin magnitudes χ1, χ2 ≤ 0.8. We used a non-parametric fitting procedure to interpolate the BMS transformations over the 3-dimensional parameter space (q, χ1, χ2). The results proposed in this model are strictly non-perturbative and cannot be obtained from post-Newtonian approximations alone, as they require knowledge of the strong nonlinear effects generated during the merger. Our work also has broad implications for studying the large-scale impact of memory effects, such as on the cosmological background.