Gravitational memory: new results from post-Newtonian and self-force theory

We compute the (displacement) gravitational wave memory due to a quasi-circular inspiral of two black holes using a variety of perturbative techniques. Within post-Newtonian theory, we extend previous results for non-spinning compact binaries to 3.5PN order. Using the gravitational self-force approach, we compute the memory at first order in the mass ratio for inspirals into a Kerr black hole. We do this both numerically and via a double post-Newtonian–self-force expansion which we carry out to 5PN order. At second order in the self-force approach, near-zone calculations encounter an infrared divergence associated with memory, which is resolved through matching the near-zone solution to a post-Minkowskian expansion in the far zone. We describe that matching procedure for the first time and show how it introduces nonlocal-in-time memory effects into the two-body dynamics at second order in the mass ratio, as was also predicted by recent 5PN calculations within the effective field theory approach. We then compute the gravitational-wave memory through second order in the mass ratio (excluding certain possible memory distortion effects) and find that it agrees well with recent results from numerical relativity simulations for near-comparable-mass binaries.