Can the Near-Horizon Black Hole Memory be detected through Binary Inspirals?
The memory effect, in the context of gravitational-waves (GWs), manifests itself in the permanent relative displacement of test masses when they encounter the GWs. A number of works have explored the possibility of detecting the memory when the source and detector are separated by large distances. A special type of memory, arising from BMS symmetries, called ``black-hole memory'', has been recently proposed. The black hole memory only manifests itself in the vicinity of its event horizon. Therefore, formally observing it requires placing a GW detector at the horizon of the BH, which prima-facie seems unfeasible. In this work, we describe a toy model that suggests a possible way the black hole memory may be observed, without requiring a human-made detector near the event horizon. The model considers a binary black hole (BBH), emanating GWs observable at cosmological distances, as a proxy for an idealized detector in the vicinity of a supermassive Schwarzschild black hole that is endowed with a supertranslation hair by sending a shock-wave to it. This sudden change affects the geometry near the horizon of the supertranslated black hole and it induces a change in the inspiraling orbital separation (and hence, orbital frequency) of the binary, which in turn imprints itself on the GWs. Using basic GW data analysis tools, we demonstrate that the black hole memory should be observable by a LISA-like space-based detector.