Toward claiming a detection of gravitational memory

TL;DR

This paper develops a theoretical framework to model and detect gravitational memory effects in gravitational wave signals, focusing on space-based detectors like LISA and mergers of supermassive black holes.

Contribution

It introduces a robust definition of the observable gravitational memory rise by separating high-frequency waves from low-frequency memory buildup, enabling better detection strategies.

Findings

Formulated a scale separation using Isaacson's energy-momentum description.

Analyzed LISA's response to gravitational memory from supermassive black hole mergers.

Provided a foundation for hypothesis testing between memory and non-memory signals.

Abstract

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.