{
  "abstract": "We give an explicit construction of all ALF and ALE toric gravitational instantons in terms of certain rational matrix functions of one complex variable on the Riemann sphere; these provide patching matrices for their corresponding twistor holomorphic vector bundles. The reconstruction of the instantons arises from the solution to a Riemann--Hilbert splitting problem and we show how this can be solved via linear algebra, resembling but not equivalent to the Belinski--Zakharov ansatz. This construction gives a complete classification together with an explicit form for all toric gravitational instantons up to the resolutions of conical and orbifold singularities. We illustrate the formalism by computer--assisted numerical construction of two new ALF (but not AF) gravitational instantons with five nodes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41867",
  "author_total": 3,
  "authors": [
    {
      "name": "Maciej Dunajski"
    },
    {
      "name": "Lionel Mason"
    },
    {
      "name": "Paul Tod"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fmhvhaxvn6msk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41867",
  "fulltext_url": null,
  "id": "fmhvhaxvn6msk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41867",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41867",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fmhvhaxvn6msk.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:15Z",
      "native_id": "2610.41867",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41867"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "The twistor construction of toric gravitational instantons",
  "title_text": "The twistor construction of toric gravitational instantons",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/fmhvhaxvn6msk",
  "venue": "arXiv",
  "versions": []
}