Fix the Frame, Resolve the Memory: The Bondi--Sachs Gauge in Black Hole Perturbation Theory

Understanding gauge and frame dependence is crucial for comparing binary models and extracting physical observables. Black hole perturbation theory calculations are extending to second-order, where increased gauge dependence brings new challenges: gauge-invariant quantities at linear order become gauge-dependent at second-order, and nonlinear source terms can produce infrared divergences.

Additionally, gravitational wave memory, a frame-dependent effect, appears at second order and will be detectable with next-generation detectors. In this seminar, I review second-order black hole perturbation theory, the Bondi--Sachs gauge, the BMS frame, and memory effects; by combining these elements, I construct a gauge invariant second-order field equation associated with an asymptotically flat gauge with the appropriate frame to extract the memory.