{
  "abstract": "We generalize the Einstein condition for Kropina metrics obtained in the positive definite setting by Zhang, Shen and others to all signatures. As examples of Einstein-Kropina metrics $L=L_{a,b}$, we construct new explicit positive definite ones and the first ones with Lorentzian signature. Next, we classify all Einstein-Kropina solutions to the vacuum equation of Finsler gravity by Pfeifer and Wohlfarth, in arbitrary dimension and including a possible cosmological constant $Λ$. For the Lorentzian and positive definite cases, the local picture is as follows. In dimension 4 or lower, only the trivial solution exists: a Minkowski or Euclidean space, essentially. In dimension 5 and higher, the solutions are those $L_{a,b}$ for which the metric $a$ is a product of the real line with a Ricci-flat metric (Lorentzian or Riemannian) and the vector field $b$ is the unique unit vector on the first factor. As a very surprising rigidity phenomenon, all Einstein-Kropina solutions to the $Λ$-vacuum equation are Berwald and Ricci-flat, and the cosmological constant necessarily vanishes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: J. Geom. Phys. 231, 105970 (2026)",
  "arxiv": "2606.07121",
  "author_total": 3,
  "authors": [
    {
      "name": "Sjors Heefer"
    },
    {
      "name": "Fidel F. Villaseñor"
    },
    {
      "name": "Andrea Fuster"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4nhx5kpaq2my7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.07121",
  "fulltext_url": null,
  "id": "4nhx5kpaq2my7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.07121",
  "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.DG"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.07121",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4nhx5kpaq2my7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:52Z",
      "native_id": "2606.07121",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.07121"
    }
  ],
  "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": "Einstein-Kropina Metrics and Their Application in Finsler Gravity",
  "title_text": "Einstein-Kropina Metrics and Their Application in Finsler Gravity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/4nhx5kpaq2my7",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.geomphys.2026.105970",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}