Black-Hole Echo Resonance Spectra and Source Dependence in a Controlled Transfer-Function Model
Abstract
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.
Versions
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BibTeX
@misc{kaminaga2026blackhole,
title = {{Black-Hole Echo Resonance Spectra and Source Dependence in a Controlled Transfer-Function Model}},
author = {Masahiro Kaminaga},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2606.03256},
eprint = {2606.03256},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.03256},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Black-Hole Echo Resonance Spectra and Source Dependence in a Controlled Transfer-Function Model
AU - Masahiro Kaminaga
PY - 2026
DA - 2026/08/04
PB - arXiv
DO - 10.48550/arxiv.2606.03256
UR - https://arxiv.org/abs/2606.03256
AB - 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.
ER -