{
  "abstract": "Black-hole critical curves and photon rings provide complementary probes of strong-field geometry, motivating a unified analytic description of these observables beyond Kerr and a direct comparison with the Kerr predictions. We develop such a description for polar observers in a radial class of stationary, axisymmetric spacetimes with separable null geodesics. The spacetime dependence is organized through natural optical combinations selected by the null dynamics and a Kerr-relative representation suited to weak deviations from Kerr. We derive compact exact expressions for the polar critical radius, Lyapunov exponent, time delay, and rotation parameter, together with general first-order formulas that can be applied once the deformation functions of a specific metric are supplied. The weak-deviation analysis shows that the combined polar observables probe only a finite set of local deformation values and radial derivatives at the critical orbit, rather than the full radial profiles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01290",
  "author_total": 3,
  "authors": [
    {
      "name": "Hao-Peng Yan"
    },
    {
      "name": "Xiang-Qian Li"
    },
    {
      "name": "Xiao-Jun Yue"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/173ct1phwms57.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01290",
  "fulltext_url": null,
  "id": "173ct1phwms57",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01290",
  "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": "W7206152465",
  "pdf_url": "https://arxiv.org/pdf/2609.01290",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/173ct1phwms57.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2609.01290",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01290"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Deviations from Kerr: Polar critical curves and photon rings in a class of separable spacetimes",
  "title_text": "Deviations from Kerr: Polar critical curves and photon rings in a class of separable spacetimes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/173ct1phwms57",
  "venue": "arXiv",
  "versions": []
}