{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.03256",
  "author_total": 1,
  "authors": [
    {
      "name": "Masahiro Kaminaga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a9avtymd8xx1f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.03256",
  "fulltext_url": null,
  "id": "a9avtymd8xx1f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.03256",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.03256",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a9avtymd8xx1f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2606.03256",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.03256"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Black-Hole Echo Resonance Spectra and Source Dependence in a Controlled Transfer-Function Model",
  "title_text": "Black-Hole Echo Resonance Spectra and Source Dependence in a Controlled Transfer-Function Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/a9avtymd8xx1f",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1142/s0218271826500537",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}