{
  "abstract": "Are the inverted Regge-Wheeler and Zerilli potentials arising in Mashhoon's bound-state approach to black-hole quasinormal modes isospectral? Extending previous numerical and analytical studies of the inverted Regge-Wheeler potential, we present the first direct computation of the bound-state spectrum of the inverted Zerilli potential. Although Chandrasekhar proved that the original potentials have identical quasinormal-mode spectra, we show that their inverted counterparts have distinct bound-state spectra. We also demonstrate that potential inversion destroys their first-order Darboux relation, used by Glampedakis et al. to provide a simpler proof of isospectrality. A continuous interpolation between the potentials reveals substantially larger energy shifts in the interior than at the endpoints, indicating cancellations that suppress the endpoint spectral splitting. Explaining this behavior requires second-order perturbative contributions, even towards the eikonal limit. Despite these differences, both spectra exhibit asymptotic geometric scaling characteristic of Efimov physics, first discovered in three-boson systems. This scaling also applies to other inverted potentials with the same leading tail, including the scalar-field case studied here. Beyond their theoretical implications, our results raise questions for recently developed methods that compute quasinormal modes with high precision from numerical bound states.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27102",
  "author_total": 2,
  "authors": [
    {
      "name": "Umer Shahzad"
    },
    {
      "name": "Sebastian H. Völkel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/at79s12bsna86.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27102",
  "fulltext_url": null,
  "id": "at79s12bsna86",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27102",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7223133797",
  "pdf_url": "https://arxiv.org/pdf/2610.27102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/at79s12bsna86.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27102"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Broken isospectrality in inverted black hole potentials and the emergence of Efimov scaling",
  "title_text": "Broken isospectrality in inverted black hole potentials and the emergence of Efimov scaling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/at79s12bsna86",
  "venue": "arXiv",
  "versions": []
}