{
  "abstract": "A localized Gaussian or Pöschl-Teller bump is widely used to probe the sensitivity of Schwarzschild quasinormal modes, where it is typically added to both the Regge-Wheeler and Zerilli potentials. We show that such an additive prescription is generically incompatible with the Darboux transformation connecting the two parity sectors. The reason is that such a transformation restricts a parity-blind bump to a fixed family of bumps with an unavoidable $r^{-2}$ tail, excluding any Gaussian or Pöschl-Teller profile with arbitrary amplitude, center, or width in the additive prescription. We give the complete classification of Darboux-admissible axial and polar pairs of bumps and propose two consistent scenarios: Darboux generator prescription in which a Gaussian or Pöschl-Teller profile is retained as a generator of the bump pair rather than as the bump itself, and Riccati completion prescription in which a Gaussian or Pöschl-Teller profile is regarded as one of the bump pair and its partner will be solved from the Riccati equation. Our frequency-domain calculations confirm that a finite and spurious axial-polar splitting of quasinormal modes will be produced if the Darboux-consistent scenarios are absent, while the centroid shift of the fundamental mode is nearly unchanged.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07323",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhen-Xiao Zhang"
    },
    {
      "name": "Chen Lan"
    },
    {
      "name": "Yan-Gang Miao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8wn68xfkzh8c2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07323",
  "fulltext_url": null,
  "id": "8wn68xfkzh8c2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07323",
  "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"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7212051197",
  "pdf_url": "https://arxiv.org/pdf/2609.07323",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8wn68xfkzh8c2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.07323",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07323"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Darboux Isospectrality Constraints on Quasinormal Modes Deformed by Bumps",
  "title_text": "Darboux Isospectrality Constraints on Quasinormal Modes Deformed by Bumps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/8wn68xfkzh8c2",
  "venue": "arXiv",
  "versions": []
}