Waveform stability of black hole ringdown with stochastic horizon structure

Abstract

We examine the robustness of black hole ringdown to stochastic horizon-scale structure within an effective field framework in a proof-of-principle Schwarzschild setup.Consistent with the understanding that the spectral instability of quasinormal modes does not necessarily imply observational breakdown, our results demonstrate that the macroscopic gravitational waveform remains robust. We identify the phase averaging mechanism as the physical origin of this stability, demonstrating that the spatial integration of the wave equation efficiently attenuates ultraviolet geometric details below the resolution limit of the probing wavelength. Building on the scaling law $\mathcal{M} \propto \epsilon^2$ and the characteristic mismatch profile with respect to $L_c$, we propose a geometric selection rule for observability: a detectable signal imposes a strict dual constraint requiring both macroscopic spatial coherence ($L_c \sim M$) and classical-level intensity ($\epsilon \gtrsim 10^{-4}$). This criterion quantitatively rules out the observability of incoherent, high-entropy quantum foam in the present static Schwarzschild model, suggesting that any significant ringdown deviation would instead serve as evidence for macroscopically coherent horizon structures.