{
  "abstract": "We study the small-c expansion of general relativity in ADM variables up to next-to-next-to-leading order (NNLO). We show that, in the stationary sector, this formulation renders the field equations more tractable for explicit solution building. The stationary equations acquire a structure, in which the leading lapse and spatial metric are determined by a closed subsystem, the NLO rotational field satisfies a linear equation on that background, and the NNLO fields satisfy a linear system sourced by the NLO data. The stationary sector exhibits both strong-gravity and weak-field branches, whose structure becomes richer at NNLO. In the strong-gravity branch, we first obtain exact vacuum solutions of NLO Carroll gravity, including the Lense–Thirring and rotating C-metric backgrounds. At NNLO, we then construct the corresponding Lense–Thirring-type and C-metric-type exact vacuum geometries. These solutions also arise from the small-c expansion of the Kerr and rotating C-metric geometries around the strong-gravity background, up to $$\\mathcal {O}(J)$$ at NLO and up to $$\\mathcal {O}(J^3)$$ at NNLO. In the weak-field branch, we find exact Hartle–Thorne-type solutions with an independent quadrupole moment, together with exact spin-squared corrections and a mixed quadrupolar-rotating solution. We further extend the $$\\ell =0,2$$ sector by including higher multipoles up to $$\\ell =4$$, where $$\\ell $$ denotes the multipole index. These results show that the full NLO/NNLO theory admits a richer stationary vacuum sector than the magnetic Carroll truncation. More broadly, the ADM formulation provides a practical framework for constructing and analyzing stationary backgrounds in the small-c expansion of general relativity, and may also offer a useful framework for organizing rotational and higher-multipole deformations motivated by relativistic compact-object geometries.",
  "abstract_shown": true,
  "affiliations": [
    "Istanbul Technical University",
    "Istanbul University-Cerrahpaşa"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Enes Bal",
      "orcid": "0009-0003-2176-9281"
    },
    {
      "affs": [
        0
      ],
      "name": "Ertuğrul Ekiz",
      "orcid": "0000-0002-8297-6706"
    },
    {
      "affs": [
        0
      ],
      "name": "Emre Onur Kahya",
      "orcid": "0000-0003-2760-7091"
    },
    {
      "affs": [
        1
      ],
      "name": "Utku Zorba",
      "orcid": "0000-0003-4645-5417"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8p15hnqzrmbq1.bib",
  "cited_by": 0,
  "doi": "10.1140/epjc/s10052-026-16509-y",
  "fulltext_url": null,
  "id": "8p15hnqzrmbq1",
  "issns": [
    "1434-6052"
  ],
  "landing_url": "https://link.springer.com/article/10.1140/epjc/s10052-026-16509-y",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "feed-journal",
      "physics/high-energy"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://link.springer.com/content/pdf/10.1140/epjc/s10052-026-16509-y.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-06",
  "publisher": "Springer Science and Business Media LLC",
  "ris": "https://research.draconitic.com/paper/8p15hnqzrmbq1.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:44Z",
      "native_id": "10.1140/epjc/s10052-026-16509-y",
      "source": "feed-springer",
      "url": "https://link.springer.com/article/10.1140/epjc/s10052-026-16509-y"
    },
    {
      "first_seen": "2026-11-06T12:20:49Z",
      "native_id": "10.1140/epjc/s10052-026-16509-y",
      "source": "crossref",
      "url": "https://link.springer.com/article/10.1140/epjc/s10052-026-16509-y"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "feed-journal:physics/high-energy",
      "subfield": "high-energy"
    }
  ],
  "title": "Stationary solutions in the small-c expansion of GR",
  "title_text": "Stationary solutions in the small-c expansion of GR",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T00:21:04Z",
  "url": "https://research.draconitic.com/paper/8p15hnqzrmbq1",
  "venue": "The European Physical Journal C",
  "versions": []
}