{
  "abstract": "We investigate how a local geometric critical point of the odd-parity Proca potential relates to the global quasibound spectrum in Schwarzschild spacetime. After normalization by $μ^2$, the axial potential $V_{\\rm ax}=(1-2M/r)[\\ell(\\ell+1)/r^2+μ^2]$ has the same radial form as the timelike-geodesic effective potential. Its outer minimum and inner maximum merge at $r=6M$, the Schwarzschild innermost stable circular orbit, when $(Mμ_c)^2=\\ell(\\ell+1)/12$. With $δ=1-(Mμ)^2/(Mμ_c)^2$, we derive exact fold scalings: stationary-point separation $\\proptoδ^{1/2}$, barrier--well depth $\\proptoδ^{3/2}$, and curvature magnitudes $\\proptoδ^{1/2}$. Continued-fraction calculations for the first three axial quasibound branches with $\\ell=1,2,3$, cross-checked for selected modes by independent Riccati shooting, show regular frequency continuation across the threshold and approximately linear near-critical behavior. At fixed radius the radial operator is affine in $δ$, supporting a conditional simple-root analytic interpretation. The main result is the explicit distinction between geometric potential criticality and spectral degeneracy for the branches examined.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34528",
  "author_total": 2,
  "authors": [
    {
      "name": "Antonio Sousa Ribeiro"
    },
    {
      "name": "Francisco Artur Pinheiro Alves Junior"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4dthpb07swfz6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34528",
  "fulltext_url": null,
  "id": "4dthpb07swfz6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34528",
  "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",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7223830997",
  "pdf_url": "https://arxiv.org/pdf/2610.34528",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4dthpb07swfz6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.34528",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34528"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Geometric criticality and regular quasibound spectra of axial Proca fields in Schwarzschild spacetime",
  "title_text": "Geometric criticality and regular quasibound spectra of axial Proca fields in Schwarzschild spacetime",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/4dthpb07swfz6",
  "venue": "arXiv",
  "versions": []
}