Graviton Echoes from Quantum Hair: A Theoretical Probe Beyond the Black Hole No-Hair Theorem

The classical no-hair theorem asserts that black holes are characterized solely by mass, charge, and angular momentum, erasing all information of the matter that formed them. However, recent advancements in quantum gravity and soft theorems suggest the existence of "soft hair" — subtle quantum structures on black hole horizons potentially encoding lost information. In this work, we propose a novel theoretical framework linking soft quantum hair with observable "graviton echoes" in the post-merger phase of black hole coalescence. We hypothesize that quantum hair configurations influence the late-time tail of gravitational wave signals, producing detectable spectral modulations distinct from classical ringdown. By modeling Planck-scale perturbations in near-horizon boundary conditions, and applying semi-classical corrections to the Einstein equations, we derive potential echo profiles embedded with quantum entanglement imprints. We further analyze their detectability within current LIGO/Virgo constraints and forecast the sensitivity required from next-generation detectors such as LISA and Einstein Telescope. Our findings open a new pathway to probe quantum information dynamics through gravitational wave astronomy, challenging the classical black hole paradigm and paving the way toward a unified understanding of spacetime microstructure.