Waveform stability of black hole ringdown with stochastic horizon structure

TL;DR

This paper investigates the stability of black hole ringdown signals against stochastic horizon-scale structures, showing that the gravitational waveform remains robust due to phase averaging, and proposes criteria for observable deviations indicating coherent horizon features.

Contribution

It introduces a geometric selection rule based on spatial coherence and intensity for the observability of horizon structures, linking waveform stability to macroscopic coherence.

Findings

Waveform remains stable despite spectral instability of quasinormal modes.

Phase averaging attenuates ultraviolet geometric details.

Detectability requires both macroscopic coherence and sufficient intensity.

Abstract

We examine the robustness of black hole ringdown to stochastic horizon-scale structure within an effective field framework. 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, suggesting that any significant ringdown deviation would serve as definitive evidence for macroscopically coherent horizon structures.