{
  "abstract": "We construct the complete spectrum of gravitational total-transmission modes (TTMs) of Kerr black holes and find four globally continuous families, $n_\\infty=1,2,3,4$, each with two complex-conjugate frequency branches. Compared with the three-family classification of Cook and Lu, our global continuation resolves the mirror-related sectors of their $n=2$ family into separate families without introducing additional symmetry-unrelated roots. This organization distinguishes complex conjugation at fixed $m$ from the mirror symmetry connecting the $m$ and $-m$ spectra. The $n_\\infty=3$ family approaches the Schwarzschild algebraically special frequency, whereas the $n_\\infty=1,2,$ and $4$ families diverge as $ω\\propto a^{-4/3}$ along lower-half-plane directions $-150^\\circ$, $-90^\\circ$, and $-30^\\circ$, respectively. High-precision data up to $\\ell=32$ confirm the Cook--Lu small-spin asymptotics and reveal how the divergent branches are embedded in the global four-family spectrum, with a family-dependent relation between the spherical-limit angular labels and the large-$|aω|$ ordering. For axisymmetric perturbations, the $n_\\infty=2$ and $n_\\infty=3$ branches coalesce at genuine exceptional points, where the scattering spectral function develops a second-order zero and the TTM excitation factors are strongly enhanced, offering a different interpretation of the structure previously described by Cook and Lu as an overtone-multiplet splitting. Finally, we identify a previously unreported anomalous proximity between the $n_\\infty=3$ TTM family and an unconventional Kerr quasinormal-mode sequence, with frequency separations reaching order $10^{-8}$ in the representative case studied.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39609",
  "author_total": 5,
  "authors": [
    {
      "name": "Changkai Chen"
    },
    {
      "name": "Xiaohua Zhang"
    },
    {
      "name": "Zhoujian Cao"
    },
    {
      "name": "Jiliang Jing"
    },
    {
      "name": "Sheng Long"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d1sjg652cyp9f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39609",
  "fulltext_url": null,
  "id": "d1sjg652cyp9f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39609",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3103|Pulsars and Gravitational Waves Research"
    ]
  ],
  "openalex": "W7215091649",
  "pdf_url": "https://arxiv.org/pdf/2609.39609",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d1sjg652cyp9f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2609.39609",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39609"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Complete total-transmission modes of Kerr black holes",
  "title_text": "Complete total-transmission modes of Kerr black holes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/d1sjg652cyp9f",
  "venue": "arXiv",
  "versions": []
}