{
  "abstract": "We formulate the closure problem for first-order, traceful radiation-gauge metric reconstruction on a Kerr background with matter. The reconstruction is decomposed into Weyl-curvature, Ricci-trace, and mass--angular-momentum completion sectors. For compatible initial, gauge, and completion data, we establish local existence and uniqueness of the resulting triangular transport system on a regular Kerr domain, and identify the additional conditions needed for a closed global formulation. This is not a global existence theorem. We test the framework using two conserved matter sources. For a thin shell around a Schwarzschild black hole, Israel matching, regularity, asymptotic flatness, a barotropic equation of state, and fixed rest mass determine the static, axial, and leading rotational sectors. The ADM-mass shift is $\\sqrt{1-2M/R}$ times the shell rest mass, while the axial sector determines the angular momentum, moment of inertia, and interior frame dragging. We also construct a stationary constant-angular-momentum fluid torus on Kerr and compute its Newman--Penrose Ricci projections, showing that nonspherical sources generally excite coupled Ricci sectors. The shell provides a closed benchmark, while the torus illustrates the additional structure required for general Kerr sources.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35938",
  "author_total": 1,
  "authors": [
    {
      "name": "G. G. L. Nashed"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9wdphz7zx73j7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35938",
  "fulltext_url": null,
  "id": "9wdphz7zx73j7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35938",
  "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"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3103|Relativity and Gravitational Theory"
    ]
  ],
  "openalex": "W7224096356",
  "pdf_url": "https://arxiv.org/pdf/2610.35938",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9wdphz7zx73j7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.35938",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35938"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Closure of Traceful Radiation-Gauge Reconstruction with Matter: General Kerr Conditions, a Thin-Shell Benchmark, and a Conserved Torus",
  "title_text": "Closure of Traceful Radiation-Gauge Reconstruction with Matter: General Kerr Conditions, a Thin-Shell Benchmark, and a Conserved Torus",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/9wdphz7zx73j7",
  "venue": "arXiv",
  "versions": []
}