Signatures of Quantum Gravity in Gravitational Wave Memory

Abstract: We study the impact of quantum corrections to gravitational waveforms on the gravitational wave memory effect. In certain quantum gravity theories and semi-classical frameworks, black holes (or other exotic compact objects) exhibit reflective properties that cause quasi-normal modes of a binary merger waveform to partially reflect off the horizon. If these reflections reach the detector, the measured gravitational wave signal may show echo-like features following the initial ringdown phase. Detecting such echoes, or their indirect signatures, would offer compelling evidence for the quantum nature of black holes. Given that direct detection of echoes requires finely tuned waveform templates, exploring alternative imprints of this phenomenon is crucial. In this work, we pursue this goal by calculating corrections to the null memory arising from echo-like features, formulated in terms of the Newman-Penrose scalar ${\Psi}_0$. We demonstrate that the morphology of the resulting features is model-independent rendering them conceptually much easier to detect in real interferometer data than the raw echo. The corresponding signal-to-noise ratio of echo-induced features appearing in the gravitational wave memory is estimated subsequently. We further compute the physical fluxes associated to the echo at both the black hole horizon and null infinity and identify novel distinguishing features of the underlying reflectivity models in measurement data.