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. While 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 associated transition. A central challenge for any claim of detection, therefore, lies in defining a physically meaningful and operationally robust model of the corresponding time-dependent signal that is uniquely attributable to gravitational memory and clearly 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 the theory of gravitational memory and focusing in particular on compact binary coalescences. Specializing to space-based detectors, we analyze the response of LISA to gravitational radiation including a memory contribution, with emphasis on mergers of supermassive black hole binaries, which offer the most promising prospects for a first single-event detection. The framework developed here 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.