{
  "abstract": "Metric perturbations obtained from a Hertz potential in an ingoing radiation gauge (IRG) generically grow in an outgoing coordinate $r$ at future null infinity, and are therefore not asymptotically flat in the Bondi sense. Hollands and Toomani showed that this growth can be removed, within the Green--Hollands--Zimmerman (GHZ) framework, by an IRG-compatible ``residual'' gauge transformation together with a carefully chosen choice of the undetermined integration ``constants'' of the Hertz potential. In this work we turn that proof into a practical algorithm. We show that this entire completion is generated by a single ``Held Master Scalar'' (HMS), which can be thought of as a function on future null infinity. The HMS is obtained from the leading asymptotic piece of the $0$-Weyl scalar through a Teukolsky--Starobinsky inversion. We give explicit formulas for the four integration constants of the Hertz potential associated with the $0$-Weyl scalar, and for the residual gauge vector in terms of the HMS, thereby bringing the metric perturbation into a Bondi-like gauge. In Schwarzschild the entire construction is diagonal in $(\\ell, m)$-modes and every completion field is available in closed form; in Kerr the construction is tri-diagonal. We have numerically implemented the full scheme in $(\\ell,m)$ and in $m$-modes, including the corrector piece of the GHZ framework. We illustrate our scheme numerically for a point-particle on a circular orbit in a puncture scheme in Schwarzschild and in Kerr, by demonstrating the Bondi-like fall-off. We also find agreement with the known Detweiler redshift computations in Schwarzschild and Kerr. Our method directly gives the Bondi news, mass-, and angular momentum aspects, for which we give exemplary results in Kerr.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06367",
  "author_total": 4,
  "authors": [
    {
      "name": "Marc Casals"
    },
    {
      "name": "Stefan Hollands"
    },
    {
      "name": "Vahid Toomani"
    },
    {
      "name": "Peter Zimmerman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7h2j2nv9vds3q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06367",
  "fulltext_url": null,
  "id": "7h2j2nv9vds3q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06367",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06367",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7h2j2nv9vds3q.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.06367",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06367"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Metric reconstruction in a Bondi-like gauge",
  "title_text": "Metric reconstruction in a Bondi-like gauge",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:20Z",
  "url": "https://research.draconitic.com/paper/7h2j2nv9vds3q",
  "venue": "arXiv",
  "versions": []
}