{
  "abstract": "Teukolsky's decoupled equations and Wald's adjoint method of metric reconstruction are built from second-order operators: the linearised Einstein operator G, the curvature-extraction operator T, the decoupled operator O and the reconstruction operator S^*, related by SG=OT. We show that on four-dimensional constant-curvature backgrounds with non-zero Lambda all of these operators factor into first-order maps through a single intermediate variable: the perturbation of the self-dual half of the spin connection. We also show that for non-zero Lambda the metric perturbation is itself obtained from the connection perturbation by a first-order map. The connection therefore gives a complete description of linearised gravity, and the fourth-order identity SG=OT follows by composition from a single second-order identity. Using conformal flatness, we choose the Hertz-potential map so that, after a conformal rescaling, the potential obeys the flat wave equation component by component. This leads to a new reconstruction scheme, in which the potential is sourced by the curvature psi, which in turn obeys a decoupled sourced equation. A prescribed curvature is then reached by a second-order rather than a fourth-order equation, and the corrector is local and algebraic in the stress-energy tensor. The price is that the full curvature, rather than a single component, must be determined, and that the reality of the reconstructed metric becomes a condition, which we argue holds for retarded solutions. We illustrate the scheme for a static point mass in de Sitter space, where it gives a real metric perturbation that agrees with linearised Schwarzschild-de Sitter up to a diffeomorphism. We view these results as a proof of concept for a first-order Teukolsky-Wald framework on Kerr.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32692",
  "author_total": 2,
  "authors": [
    {
      "name": "Kirill Krasnov"
    },
    {
      "name": "Adam Shaw"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dqha4fzemm8t4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32692",
  "fulltext_url": null,
  "id": "dqha4fzemm8t4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32692",
  "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"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3103|Relativity and Gravitational Theory"
    ]
  ],
  "openalex": "W7223663005",
  "pdf_url": "https://arxiv.org/pdf/2610.32692",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dqha4fzemm8t4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2610.32692",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32692"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "First-Order Structure of the Linearised Einstein Equations: Constant-Curvature Backgrounds",
  "title_text": "First-Order Structure of the Linearised Einstein Equations: Constant-Curvature Backgrounds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:15Z",
  "url": "https://research.draconitic.com/paper/dqha4fzemm8t4",
  "venue": "arXiv",
  "versions": []
}