{
  "abstract": "Helicity in gravity is a multifaceted concept, and several inequivalent definitions exist in the literature. In this work, we reduce the topological Pontryagin and Nieh-Yan terms to a constant time spacelike hypersurface. Remarkably, upon applying the SVT decomposition at the linearized level, we obtain four distinct helicity densities. The helicity density arising from the Nieh-Yan term is termed the spin-1 and spin-2 gravitomagnetic helicity density, depending on whether it originates from vector or tensor modes. Meanwhile, the helicity density arising from the Pontryagin term is termed the spin-1 and spin-2 gravito-current helicity density, according to the corresponding mode contributions. We study the mode and multipole expansions of these helicity functionals and apply them to leading order Newtonian two-body systems, weak field boosted Kerr, a locally defined slowly varying gyratonic pp-wave model, and a linearized gravitational Hopfion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30154",
  "author_total": 4,
  "authors": [
    {
      "name": "Hongxi Huang"
    },
    {
      "name": "Jiang Long"
    },
    {
      "name": "Gan Zhao"
    },
    {
      "name": "Xin-Hao Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/asx5gwtx9yyas.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30154",
  "fulltext_url": null,
  "id": "asx5gwtx9yyas",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30154",
  "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",
      "3103|Relativity and Gravitational Theory"
    ]
  ],
  "openalex": "W7204957173",
  "pdf_url": "https://arxiv.org/pdf/2608.30154",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/asx5gwtx9yyas.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.30154",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30154"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Spacelike reduction of the gravitational topological terms and associated helicity densities",
  "title_text": "Spacelike reduction of the gravitational topological terms and associated helicity densities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/asx5gwtx9yyas",
  "venue": "arXiv",
  "versions": []
}