{
  "abstract": "We establish a scale-invariant spatial non-collapse estimate for hypersurface-orthogonal timelike geodesic congruences. The result extends a previous Raychaudhuri-based construction in which a comparison estimate for the expansion was used to control the volume of domains transported along the congruence. The additional ingredient here is a quantitative estimate of the spatial distance distortion induced by the expansion and shear. Assuming that the initial spatial geometry is non-collapsed up to a scale $r_0$, and that the expansion, shear, and timelike Ricci curvature satisfy suitable uniform bounds, we obtain, before the first blow-up time of the Raychaudhuri comparison solution, \\begin{equation*} \\operatorname{Vol}_{h_τ}\\bigl(B_{h_τ}(p_τ,r)\\bigr) \\geq κ_{\\mathrm{L}}(τ)\\, r^3, \\end{equation*} where \\begin{equation*} κ_{\\mathrm{L}}(τ) = κ_0 e^{-3Kτ} \\exp\\!\\left(\\int_0^τΘ(s)\\,ds\\right), \\qquad K = \\frac{Θ_0}{3} + Σ_0 . \\end{equation*} Here $Θ$ denotes the solution of the scalar Raychaudhuri comparison equation and $K$ controls the spatial metric distortion. For every finite time strictly before the comparison barrier, $κ_{\\mathrm{L}}(τ)$ is positive. When the comparison solution has a finite blow-up time, the explicit comparison coefficient approaches zero as that time is approached from below. The comparison barrier is a boundary of the estimate and is not, by itself, a statement that the physical congruence develops a focal point or spacetime singularity. The result is structurally analogous to scale-invariant non-collapse estimates in geometric flow, but is mathematically distinct from Perelman's $κ$-noncollapsing theorem for Ricci flow.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Physics Letters B Date: November 2026 Article: 140987 Volume: Volume 882",
  "arxiv": "2610.07879",
  "author_total": 1,
  "authors": [
    {
      "name": "Rohit Dhormare"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/55revvecctx1w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07879",
  "fulltext_url": null,
  "id": "55revvecctx1w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07879",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.07879",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/55revvecctx1w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.07879",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07879"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Scale-Invariant Non-Collapse from Raychaudhuri Comparison",
  "title_text": "Scale-Invariant Non-Collapse from Raychaudhuri Comparison",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/55revvecctx1w",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.physletb.2026.140987",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}