{
  "abstract": "We prove the Hawking and Penrose singularity theorems for Lorentz--Finsler structures of mixed horizontal/vertical regularity $C^{(1,2)}$ in the $C^1$ weighted case and $C^{(1,3)}$ in the unweighted case. At this regularity, geodesics need not be uniquely determined by their initial conditions, and the (weighted) Ricci curvature must be interpreted distributionally. Our approach relies on a two-stage approximation procedure: first, a homogeneity-preserving convolution, which is of independent interest in the broader semi-Riemann--Finsler setting, and second, a causality-adapted approximation à la Chruściel--Grant. In the special case of $C^1$ Lorentzian metrics, our results extend the $C^1$ singularity theorems of Graf to the $C^1$ weighted case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11911",
  "author_total": 4,
  "authors": [
    {
      "name": "Darius Erös"
    },
    {
      "name": "Ettore Minguzzi"
    },
    {
      "name": "Argam Ohanyan"
    },
    {
      "name": "Shin-ichi Ohta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3q33jyphvwkw7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11911",
  "fulltext_url": null,
  "id": "3q33jyphvwkw7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11911",
  "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"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7221131845",
  "pdf_url": "https://arxiv.org/pdf/2610.11911",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3q33jyphvwkw7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.11911",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11911"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "The Hawking and Penrose singularity theorems for low regularity Finsler spacetimes",
  "title_text": "The Hawking and Penrose singularity theorems for low regularity Finsler spacetimes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/3q33jyphvwkw7",
  "venue": "arXiv",
  "versions": []
}