A Computable Near-Horizon Boundary Model for Black Hole Ringdown: Observational Constraints and WKB Eigenvalue Matching in the ZIP Framework

This work develops a conservative and falsifiable effective formulation of the ZIP coherence framework in the context of black hole ringdown physics.

Starting from current observational bounds including gravitational wave ringdown consistency with Kerr predictions, the absence of statistically robust echo detections, and tidal deformability constraints we translate empirical limits into constraints on a minimal set of phenomenological ZIP boundary parameters.

We then replace the previously phenomenological echo transmission factor by an explicit WKB barrier treatment based on the Regge–Wheeler potential. This yields a computable near-horizon cavity model with a partially reflecting boundary located outside the classical horizon. A closed eigenvalue matching condition is formulated, providing a direct inference map from observable quantities (echo delay, amplitude scaling) to boundary microphysics parameters.

The construction preserves the Kerr/Schwarzschild exterior at leading order and reduces smoothly to the general relativity limit as reflectivity and transition width vanish. The framework defines clear falsifiability criteria for next-generation detectors such as LISA, Einstein Telescope, Cosmic Explorer, and ngEHT.

This paper establishes a concrete bridge between phenomenological near-horizon modifications and a computable eigenvalue problem, positioning the ZIP framework as an effective boundary model testable through gravitational wave spectroscopy.