Analytically Modeling Gravitational-Wave Memory with SEBOB: A Unified Effective and Backwards One-Body Approach

Non-linear gravitational wave memory effects, arising from gravitational wave energy flux, result in the permanent displacements between a set of test masses after a wave passes by. We model this displacement memory effect by leveraging the Backwards One-Body Model (BOB), an analytical, first-principles model for merger-ringdown characterized by perturbations of the remnant Kerr black hole. We use BOB in conjunction with the Effective One-Body (EOB) framework which models the preceding inspiral. The unified Spinning Effective-to-Backwards One Body (SEBOB) formalism yields a physically motivated description of memory throughout the inspiral, merger, and ringdown. Using this framework, we determine the memory effect via two different methods: we adapt a time-dependent formula for memory derived from multipole moments from Favata (2010), and we exploit the Bondi-vanderBurg-Metzner-Sachs (BMS) balance laws. We find that our physically-motivated memory models are in excellent agreement with the memory effects present in numerical relativity simulations from the Simulating eXtreme Spacetimes (SXS) Collaboration's catalog.