{
  "abstract": "Bianchi spacetimes are usually written in separated form: metric coefficients depend only on cosmic time, while spatial dependence is carried by an invariant coframe. In this representation, geometric quantities and the Einstein equations reduce to a time-dependent system. In practice, however, observer- and gravitational-wave-adapted gauges mix time and space (e.g., from integrability-adapted to synchronous comoving coordinates). Homogeneity is preserved, but separability is no longer manifest, which complicates computation. To address this, we give a gauge-invariant reconstruction of separated frames using only the spatial Killing algebra. Given a basis $\\{ξ_a\\}$, we construct an invariant spatial frame $\\{X_i\\}$ from $[ξ_a,X_i]=0$, then dualize to $\\{e_i\\}$. The metric then takes the canonical form $g=γ_{μν}(t) e^μe^ν$ in any gauge. We prove diffeomorphism covariance of the construction, and demonstrate computational gain in a Bianchi II example. The framework recovers canonical adapted-gauge constructions (in the sense of Jantzen) while remaining stable under arbitrary $\\operatorname{Diff}(M)$ gauge transformations, and is directly suited to gravitational-wave Bianchi models and related exact solutions of recent interest of which we give a example of the Bianchi VII type.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31887",
  "author_total": 2,
  "authors": [
    {
      "name": "Dave B. H. Verweg"
    },
    {
      "name": "Robbert W. Scholtens"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2agshfzt4mw3q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31887",
  "fulltext_url": null,
  "id": "2agshfzt4mw3q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31887",
  "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|Relativity and Gravitational Theory"
    ]
  ],
  "openalex": "W7223666481",
  "pdf_url": "https://arxiv.org/pdf/2610.31887",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2agshfzt4mw3q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2610.31887",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31887"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Gauge Invariant Frames of Bianchi Models in Separated Form",
  "title_text": "Gauge Invariant Frames of Bianchi Models in Separated Form",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:15Z",
  "url": "https://research.draconitic.com/paper/2agshfzt4mw3q",
  "venue": "arXiv",
  "versions": []
}