Toward claiming a detection of gravitational memory

Gravitational memory is a zero-frequency effect associated with a permanent change in the asymptotic spacetime metric induced by radiation. Although its universal manifestation is a net change in the proper distances between freely falling test masses, gravitational wave detectors are intrinsically insensitive to the final offset and can only probe the transition. A central challenge for any detection claim is therefore to define a physically meaningful and operationally robust model of the time-dependent signal that is uniquely attributable to gravitational memory and distinguishable from purely oscillatory radiation. We show that while the Bondi-van der Burg-Metzner-Sachs balance laws rigorously establish the total memory offset, a robust definition of the observable memory rise requires an additional physical input: a separation of scales between high-frequency gravitational waves and the lower-frequency buildup of memory. We formulate this separation using the Isaacson description of gravitational wave energy momentum. Motivated by this observation, we develop a theoretical framework for defining and modeling the time-dependent memory rise, building on a self-contained review of gravitational memory and focusing on compact binary coalescences. Specializing to space-based detectors, we analyze the LISA response to gravitational radiation including memory, with emphasis on mergers of supermassive black hole binaries, which offer the most promising prospects for a first single-event detection. The framework provides the theoretical foundation for statistically well-defined hypothesis testing between memory-free and memory-full radiation and enables quantitative assessments of detection prospects. These results establish a principled pathway toward a future observational claim of gravitational memory.