{
  "abstract": "Null homogeneous Petrov spaces $V^*_4(N)$ are considered. The geometry of $V^*_4(N)$ is determined by the geometry of the three-dimensional homogeneous Riemannian space $V_3(N)$, which is invariant under the action of the three-parameter motions group $G_3(N)$ ($N$ corresponds to the group number in the Bianchi classification). The canonical frame of the space $V_3(N)$ is used to construct the metric tensor of the space $V^*_4(N)$ and the components of the vector potential of the invariant electromagnetic field. Using this reper, we obtain Maxwell vacuum equations containing only the structure constants of the groups, the non-holonomic components of the contravariant metric tensor and vector potential, and their derivatives with respect to the wave variable. All non-equivalent exact solutions of Maxwell vacuum equations are found for the case of solvable motions groups $G_3(I)-G_3(VII)$. All solutions of Maxwell vacuum equations obtained in this article are written explicitly in terms of arbitrary independent functions of wave variable. Therefore, when integrating the Einstein-Maxwell equations, it has to consider only the remaining systems of Einstein equations which reduce to systems of ordinary differential equations that include only these independent functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04522",
  "author_total": 1,
  "authors": [
    {
      "name": "V. V. Obukhov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fwar79v2h4tea.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04522",
  "fulltext_url": null,
  "id": "fwar79v2h4tea",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04522",
  "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"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7220686579",
  "pdf_url": "https://arxiv.org/pdf/2610.04522",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fwar79v2h4tea.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.04522",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04522"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Exact solutions of Maxwell vacuum equations in null homogeneous Petrov spaces with solvable motions groups",
  "title_text": "Exact solutions of Maxwell vacuum equations in null homogeneous Petrov spaces with solvable motions groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/fwar79v2h4tea",
  "venue": "arXiv",
  "versions": []
}