Inferring fundamental spacetime symmetries with gravitational-wave memory: from LISA to the Einstein Telescope

We revisit gravitational wave (GW) memory as the key to measuring spacetime symmetries, extending beyond its traditional role in GW searches. In particular, we show how these symmetries may be probed via displacement and spin memory observations, respectively. We further find that the Einstein Telescope's (ET) sensitivity enables constraining the strain amplitude of a displacement memory to 2% and that of spin memory to 22%. Finally, we point out that neglecting memory could lead to an overestimation of measurement uncertainties for parameters of binary black hole (BBH) mergers by about 10% in ET.