{
  "abstract": "How precisely must a photon's impact parameter be tuned for it to complete $n$ windings around a nearly extremal Kerr black hole before escaping, and how does the same near extremal scaling control the focusing of neighboring rays? For equatorial prograde returns we find, with $κ=\\sqrt{1-a^2/M^2}$ and $X=nκ$, $ε_n=\\sqrt{3}\\,κ/(e^{2πX}-1) +O(κ^2|\\lnκ|)$. This single law connects the extremal inverse-winding hierarchy to subextremal exponential accumulation. Perturbing the return family quasi-equatorially, we derive a second scaling law for the polar Jacobi phase, $Ψ_θ=2\\ln[\\sinh(πX)/κ]+C_s+o(1)$, and show that its focusing points cross from geometric spacing in winding number to asymptotically uniform spacing $Δ\\mathcal N\\simeq(2κ)^{-1}$. Numerical integrations of the exact Kerr radial dynamics and linear polar equation verify both scaling collapses. Thus near extremal Kerr exhibits parametrically distinct winding and polar-focusing scales, rather than a discontinuous jump between extremal and subextremal lensing hierarchies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21848",
  "author_total": 3,
  "authors": [
    {
      "name": "Valentina Gonzalez-Moya"
    },
    {
      "name": "Ali Ovgun"
    },
    {
      "name": "Joel Saavedra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/30z18s7sn27xg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21848",
  "fulltext_url": null,
  "id": "30z18s7sn27xg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21848",
  "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",
      "3103|Astrophysical Phenomena and Observations"
    ]
  ],
  "openalex": "W7222593270",
  "pdf_url": "https://arxiv.org/pdf/2610.21848",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/30z18s7sn27xg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.21848",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21848"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Photon-Return and Polar-Focusing Crossovers near Extremal Kerr",
  "title_text": "Photon-Return and Polar-Focusing Crossovers near Extremal Kerr",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:50Z",
  "url": "https://research.draconitic.com/paper/30z18s7sn27xg",
  "venue": "arXiv",
  "versions": []
}