{
  "abstract": "The conservation law for the orbital plus spin angular momentum of a free Dirac particle in curved spacetime requires that the affine connection has the antisymmetric part: the torsion tensor, which extends general relativity to the Einstein$-$Cartan theory of gravity. In spacetime with torsion, the Dirac equation becomes a nonlinear, cubic equation in the spinor wave function. Under charge conjugation, the nonlinear term changes sign relative to the mass term. A Dirac spinor and its charge conjugate therefore satisfy different field equations. We use the spinor connection formalism to derive the Dirac equation for a spherical spinor in its centrally symmetric gravitational field with torsion. We determine the energy$-$momentum tensor for this spinor and show that the energy contribution from torsion is negative for matter particles and positive for antimatter particles. Consequently, the ground state of a fermion has a lower energy than the ground state of the corresponding antifermion. We also derive the Einstein$-$Cartan$-$Dirac equations for this spinor; they indicate the existence of particle-like soliton solutions exhibiting matter$-$antimatter energy asymmetry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38738",
  "author_total": 1,
  "authors": [
    {
      "name": "Nikodem Popławski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/784wxztrf3qkn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38738",
  "fulltext_url": null,
  "id": "784wxztrf3qkn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38738",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38738",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/784wxztrf3qkn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.38738",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38738"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Gravitational field of spinors with torsion and matter$-$antimatter asymmetry",
  "title_text": "Gravitational field of spinors with torsion and matter−antimatter asymmetry",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:50Z",
  "url": "https://research.draconitic.com/paper/784wxztrf3qkn",
  "venue": "arXiv",
  "versions": []
}