{
  "abstract": "Since Brill's work of 1959, the conformal factor of finite-amplitude Brill waves, the axisymmetric and time-symmetric vacuum initial data on $\\mathbb{R}^3$ that describe pure gravitational radiation, has been obtained only numerically, up to the most recent studies. Here an explicit one-parameter family of such data is constructed: the first explicit real-analytic, non-trivial, asymptotically flat vacuum initial data with trivial topology and a single end. The free metric function is a closed-form combination of elementary functions and a dilogarithm. The data have the toroidal conformal symmetry of Beig and Husa, and a change of variable of Natanzon type reduces every mode equation to the Gauss hypergeometric equation, so that the conformal factor is a series with explicit Gamma-function coefficients. The quantities that have so far required numerical work are thereby obtained exactly. A ground-state identity gives a sharp existence criterion: complete, asymptotically flat data exist precisely for $k<k_c=0.8048016772\\ldots$, and the explicit series is identified with the unique variational solution. The ADM mass is an absolutely convergent digamma series, with $m/a=πk^2/10+O(k^3)$ for small amplitudes and an explicit residue at its critical divergence. Sufficiently strong waves contain trapped surfaces: it is proved that for $k$ close to $k_c$ the rescaled conformal factor converges to an explicit function and explicit tori and spheres become outer trapped, so that the data contain an apparent horizon. A numerical search, restricted to equatorially symmetric star-shaped surfaces, finds marginally trapped (minimal) spheres, which appear in a fold near $k=0.7670$. No thin-torus or weak-field approximation is used.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16773",
  "author_total": 1,
  "authors": [
    {
      "name": "Piotr Koc"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5k9ngz3ke8jbc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16773",
  "fulltext_url": null,
  "id": "5k9ngz3ke8jbc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16773",
  "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"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3103|Relativity and Gravitational Theory"
    ]
  ],
  "openalex": "W7221817614",
  "pdf_url": "https://arxiv.org/pdf/2610.16773",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5k9ngz3ke8jbc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.16773",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16773"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Analytic Brill wave initial data with trapped surfaces",
  "title_text": "Analytic Brill wave initial data with trapped surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:16Z",
  "url": "https://research.draconitic.com/paper/5k9ngz3ke8jbc",
  "venue": "arXiv",
  "versions": []
}