Influence of quantum decoherence on black hole shadow visibility and time domain echoes

Abstract

The geometric shadow of a black hole cannot observationally distinguish horizonless exotic compact objects. We break this degeneracy by mapping the fundamental quantum decoherence of the horizon (the Danielson-Satishchandran-Wald mechanism) into a macroscopic effective reflectivity $\mathcal{R}$. Utilizing Kerr ray tracing, we show that a partially reflective boundary ($\mathcal{R}>0$) generates delayed electromagnetic echoes under both specular and diffuse (Lambertian) conditions. In the spatial domain, these echoes illuminate the inner shadow and alter low-frequency visibilities, while leaving metric-governed photon subrings unchanged. The signal strength scales with the membrane compactness $\epsilon$ as ${\epsilon }^{\Gamma }$, where $\Gamma =0$ for specular reflection and $\Gamma \to 1$ for diffuse re-emission due to escape-cone collapse. This brings specular reflectivities down to $\mathcal{R}\simeq 0.12$ (ngEHT) and $0.04$ (BHEX) within reach of static imaging. For Sagittarius A${}^{\ast }$, we translate these echoes into a robust time-domain signature. Using an Autocorrelation Function (ACF) pipeline, we demonstrate that single-flare echoes can be cleanly extracted from severe accretion red noise, achieving a $3\sigma$ detection for amplitudes $\mathcal{A}\gtrsim 0.3$ within 15 to 33 hours of continuous monitoring. This framework provides a directly deployable pathway to test black hole unitarity.

18 pages, 11 figures