Low finesse scattering and spectral drift of gravitational wave echoes

Abstract: Gravitational wave echoes serve as probes for quantum horizon corrections. While steady-state resonances are assumed in the search of gravitational wave echos, realistic barriers are expected to possess intrinsically low reflectivity. In this work, we investigate this low-finesse limit via time-domain simulations and demonstrate that early-time echoes behave as transient scattered wave packets rather than cavity eigenstates. A central finding is the identification of spectral drift, where the central frequency progressively redshifts. This evolution occurs because high-frequency components dissipate significantly faster than the fundamental mode due to the filtering effect of the potential barrier. To distinguish transient interference from genuine resonance, we establish a physical criterion based on cavity lifetime, identifying a critical reflectivity threshold of approximately $0.37$. Since theoretical models typically operate deep within the overdamped regime below this limit, the resulting signals are spectrally non-stationary. We propose that detection strategies should shift towards dynamic time-frequency tracking to capture these drifting signatures.