{
  "abstract": "The X-ADM mass is a generalisation of the ADM mass for asymptotically flat manifolds, recently introduced by Mantegazza and Oronzio [arXiv:2602.11372], who proved a positive mass theorem for this quantity in dimension $3$ under a certain topological condition. In this article, we prove the X-positive mass theorem with rigidity in all dimensions $n\\geq3$ without any topological restrictions. To this end, we first prove that the scalar curvature condition appearing in the X-positive mass theorem implies the metric is of positive Yamabe type. We then show that the X-ADM mass of the given metric is equal to the ADM mass of a scalar-flat representative in its conformal class plus a term that is explicitly non-negative. From this, the X-positive mass theorem follows from the standard positive mass theorem. As a corollary, we obtain the Riemannian mass--charge inequality of general relativity in all dimensions, which was previously only known for spin manifolds. Finally, we give a version of the X-positive mass theorem for a manifold with boundary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.03629",
  "author_total": 1,
  "authors": [
    {
      "name": "Stephen McCormick"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/32zj008pbamhs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.03629",
  "fulltext_url": null,
  "id": "32zj008pbamhs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.03629",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7167618297",
  "pdf_url": "https://arxiv.org/pdf/2607.03629",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/32zj008pbamhs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2607.03629",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.03629"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "A conformal reduction for the X-ADM mass",
  "title_text": "A conformal reduction for the X-ADM mass",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/32zj008pbamhs",
  "venue": "arXiv",
  "versions": []
}