{
  "abstract": "Thermodynamic rewritings of horizon equations depend on which relations are varied and which have already been imposed. We formulate a differential rank criterion that makes these choices explicit. The construction uses a stationary metric family together with an independently marked radial surface, physical charges determined by the metric parameters, and specified extensions of the horizon thermodynamic quantities. A first-law covector is pointwise representable by selected constraints precisely when it lies in the span of their differentials. We distinguish this algebraic condition from a smooth identity in a neighborhood. If regular constraints already define the complete physical family, pointwise representability follows from the first law itself; a neighborhood identity additionally depends on the chosen extensions. With explicit prescriptions, Kerr--Newman, rotating BTZ black holes in new massive gravity, and the new-type NMG black hole all exhibit exact alignment with their horizon constraints. By contrast, substituting an exact metric family into a field-equation component can annihilate that residual before any horizon condition is tested. We also give an explicit entropy--volume comparison and specify the role of fixed ensemble data in free-energy variations. The framework separates consequences of the established first law from additional claims about selected constraints and their extensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16571",
  "author_total": 1,
  "authors": [
    {
      "name": "Gunn Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ej19etfzxj2k6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16571",
  "fulltext_url": null,
  "id": "ej19etfzxj2k6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16571",
  "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"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7213413913",
  "pdf_url": "https://arxiv.org/pdf/2609.16571",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ej19etfzxj2k6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.16571",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16571"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Black-Hole First Laws and Horizon Constraints: A Differential Rank Criterion",
  "title_text": "Black-Hole First Laws and Horizon Constraints: A Differential Rank Criterion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:41Z",
  "url": "https://research.draconitic.com/paper/ej19etfzxj2k6",
  "venue": "arXiv",
  "versions": []
}