{
  "abstract": "We consider whether the translation Noether current of a linearised metric spin-2 theory admits a strictly gauge-invariant local representative. For Fierz-Pauli and dynamically regular pure curvature-squared theories in four dimensions, we show that no such representative exists under the stated locality, polynomiality and covariance assumptions. A direct enumeration first excludes nonzero symmetric rank-two tensors at the dimension and derivative order of the quadratic action: in the curvature-squared case, the parity-even conservation kernel consists of the identically vanishing Lanczos--Lovelock combination, while both parity-odd coefficients vanish. Homogeneity of the actions in total derivative number then allows projection by field degree and derivative number, extending the exclusion to all finite-order local polynomial representatives with constant coefficients and no explicit coordinate dependence. The translation current nevertheless defines a nonzero conserved-current class. Independently, a constant translation is a Killing reducibility parameter of the linearised gauge symmetry and determines a nonzero linear surface-charge class, which is distinct from the quadratic energy current. A separate calculation shows why a direct compensator cancellation available in Maxwell theory fails for the metric spin-2 field, although this calculation is not needed for the current-class result. Maxwell theory, propagating free $p$-forms and Yang--Mills theory linearised about the trivial vacuum provide comparisons in which translations are not reducibility parameters and strictly gauge-invariant stress tensors exist. Gauss--Bonnet and pure flat-space $R^2$ gravity lie outside the regular scope of the result, through variational triviality and dynamical degeneracy, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13700",
  "author_total": 3,
  "authors": [
    {
      "name": "Michael Hobson"
    },
    {
      "name": "Will Barker"
    },
    {
      "name": "Anthony Lasenby"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ftdxv4kweqc15.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13700",
  "fulltext_url": null,
  "id": "ftdxv4kweqc15",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13700",
  "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": "W7221521297",
  "pdf_url": "https://arxiv.org/pdf/2610.13700",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ftdxv4kweqc15.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.13700",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13700"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Bessel-Hagen currents, reducibility charges, and local gravitational energy",
  "title_text": "Bessel-Hagen currents, reducibility charges, and local gravitational energy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:36Z",
  "url": "https://research.draconitic.com/paper/ftdxv4kweqc15",
  "venue": "arXiv",
  "versions": []
}