Gauge-Invariant Signatures of Adiabatic Quantum Hair in Time-Resolved Black Hole Shadows and Ringdown

Abstract

Black hole shadows and gravitational-wave ringdown provide complementary probes of strong-field gravity and the near-horizon geometry of compact objects. We develop a controlled semiclassical framework in which slowly evolving horizon degrees of freedom (“quantum hair” in an effective description), associated with effective horizon charges, generate gauge-invariant perturbations of Kerr spacetime within a two-timescale expansion. This construction preserves leading-order geodesic separability while allowing adiabatic evolution of the horizon variables. We derive first-order corrections to the photon sphere, polarization transport, and quasi-normal mode (QNM) spectrum, and show that these observables are governed by the same set of semiclassical horizon parameters. This leads to a dimensionless multi-messenger consistency relation linking shadow deformations and ringdown frequency shifts, providing a correlated signature that distinguishes the framework from generic phenomenological deviations from Kerr geometry. We further formulate a Bayesian inference framework for constraining the effective horizon parameters and present a proof-of-principle parameter inference experiment on synthetic data to illustrate the information content of the proposed observables. Although the predicted corrections are strongly Planck suppressed for astrophysical black holes, the formalism provides a systematic effective field theory framework for placing observational bounds on enhanced semiclassical horizon scenarios using future very-long-baseline interferometry and gravitational-wave measurements.