{
  "abstract": "The classification of relativistic closed orbits by their multileaf structures provides a framework for studying strong-field dynamics. Identifying these structures in astronomical images remains challenging. Using ray tracing, we construct the spatiotemporal autocorrelations of the primary image of a pointlike hotspot moving along bound closed geodesics around a Schwarzschild black hole. These orbits are classified by three integers $(z,w,v)$, where $z$ counts the leaves, $w$ counts the additional whirls during each radial period, and $v$ specifies the order in which the orbital leaves are traced. For the orbit families examined, our numerical results establish a correspondence between the topological integers $(z,w,v)$ and the numbers of correlation bands $N_{\\rm band}$ and recurrence points $N_{\\rm rec}$. The integers are recovered as $z=N_{\\rm rec}-1$, $w=\\left\\lfloor (N_{\\rm band}+1)/(N_{\\rm rec}-1)\\right\\rfloor-1$, and $v=(N_{\\rm band}+1)\\bmod(N_{\\rm rec}-1)$. Here, $\\lfloor x\\rfloor$ denotes the greatest integer not exceeding $x$, and $\\bmod$ denotes the remainder operation. These relations provide a quantitative method for recovering closed-orbit topology from hotspot image autocorrelations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36767",
  "author_total": 3,
  "authors": [
    {
      "name": "Fengting Xie"
    },
    {
      "name": "Qing-Hua Zhu"
    },
    {
      "name": "Xin Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2mx1s05fgktp4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36767",
  "fulltext_url": null,
  "id": "2mx1s05fgktp4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36767",
  "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"
    ],
    [
      "openalex",
      "3103|Astrophysical Phenomena and Observations"
    ]
  ],
  "openalex": "W7214940192",
  "pdf_url": "https://arxiv.org/pdf/2609.36767",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2mx1s05fgktp4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.36767",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36767"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Correspondence between multileaf topology of closed geodesics and spatiotemporal autocorrelations of hotspot images in Schwarzschild spacetime",
  "title_text": "Correspondence between multileaf topology of closed geodesics and spatiotemporal autocorrelations of hotspot images in Schwarzschild spacetime",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/2mx1s05fgktp4",
  "venue": "arXiv",
  "versions": []
}