2026/06/30 by Masahiro Kaminaga
Physics and Astronomy · #gr-qc
27 pages, 8 figures (12 panels in total)
arxiv created 2026/08/04 · arxiv updated 2026/08/05
Echo models phenomenologically encode possible near-horizon structure by replacing the purely ingoing horizon-side condition with an effective reflecting inner boundary near the would-be horizon. We study this idea in a controlled transfer-function model consisting of a compactly supported one-dimensional barrier and a Robin wall at x=-L, where L>0 is the cavity length measured in the tortoise coordinate. The aim is not to propose a new echo mechanism or to make an observational claim, but to analyze the standard cavity denominator in a controlled model with explicit normalizations. For this model, we prove a local one-zero-per-cell result with an O(L-2) localization error and derive a source-to-observer factorization which separates the homogeneous poles from the source-dependent residues. To test the physical robustness of the mechanism, we also perform direct numerical calculations for the untruncated axial Regge-Wheeler potential. The computed resonances form the same nearly equally spaced comb, their deviations from the first asymptotic centers are numerically consistent with L-2 scaling, and smooth source profiles modify the peak weights without changing the homogeneous pole locations. The rigorous O(L-2) theorem remains restricted to the compactly supported model.