{
  "abstract": "Buchdahl transformations provide a geometric route from vacuum spacetimes to scalar-field solutions. We formulate this mechanism as a target-covariant solution generator for Einstein gravity coupled to nonlinear sigma models in $D>3$ dimensions. On any connected region in which a Ricci-flat seed admits a non-null hypersurface-orthogonal cyclic coordinate with fixed-sign nonzero norm, the logarithm of that norm defines a Buchdahl potential $Σ$. A one-parameter redistribution of the cyclic norm then generates the exact Ricci source $R_{AB}=C_D(β)\\partial_AΣ\\partial_BΣ$, with $C_D(β)=\\frac{D-2}{D-3}(1-β^2)$, while $Σ$ remains harmonic in the deformed metric. Composing $Σ$ with an affinely parametrized geodesic of a non-degenerate target metric whose squared speed is $C_D(β)$ therefore yields an exact Einstein--sigma-model solution. For positive-definite targets, the corresponding pullback condition also implies that the nontrivial scalar map has one-dimensional image; for indefinite targets, the geodesic ansatz remains a sufficient solution-generating sector but need not exhaust all possible realizations of the same rank-one spacetime source. Through the Einstein/Jordan-frame correspondence, the construction gives vacuum tensor--multiscalar solutions as well. We illustrate the unified generator with flat, spherical, hyperbolic and axion--dilaton targets and with Tangherlini, Weyl, Kasner, Rosen-wave, Gowdy, Kaluza--Klein bubble and C-metric seeds. The result separates cleanly the geometric Buchdahl source from its target-space realization and extends this rank-one cyclic sector across static, cosmological, wave and accelerating geometries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phys.Rev.D 114 (2026) 10, 104015",
  "arxiv": "2608.20180",
  "author_total": 3,
  "authors": [
    {
      "name": "David S. Pereira"
    },
    {
      "name": "Francisco S. N. Lobo"
    },
    {
      "name": "José Pedro Mimoso"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9m8kt0ebeztz4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.20180",
  "fulltext_url": null,
  "id": "9m8kt0ebeztz4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.20180",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2608.20180",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9m8kt0ebeztz4.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2608.20180",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.20180"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "A Buchdahl solution generator for Einstein-sigma gravity and multiscalar-tensor gravity",
  "title_text": "A Buchdahl solution generator for Einstein-sigma gravity and multiscalar-tensor gravity",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:34Z",
  "url": "https://research.draconitic.com/paper/9m8kt0ebeztz4",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/9y7s-fvxg",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}