{
  "abstract": "The ideal magnetohydrodynamic (MHD) system that governs a conducting plasma---the Maxwell equations together with the conservation laws of mass, momentum and energy---is the same local balance structure that describes hot accretion flows around black holes. We introduce a uniform four-dimensional spacetime dilation \\[ Φ_L:\\;(t',x',y',z')\\mapsto (t,x,y,z)=(Lt',Lx',Ly',Lz'),\\qquad L>1, \\] and show that it is a smooth, orientation-preserving $C^\\infty$ diffeomorphism of flat spacetime. Pulling the MHD conservation laws back through $Φ_L$, we prove that the closed ideal-MHD system is form-invariant (covariant), with the current density rescaling as $\\bm j=\\bm j'/L$, the magnetic diffusivity as $η'=η/L$, and external sources rescaled by $L$. The transformation realises three physically distinct effects on the perturbed flow: a \\emph{linearization} to the tangent-space (linearised MHD) system, a \\emph{movie slow-motion} dilation of dissipative and dynamical timescales, and an \\emph{electron-microscope} magnification of small-scale structure. Taking the formal limit $L\\to\\infty$ localises the dynamics on a neighbourhood of a horizon: resistivity vanishes, the asymptotic time derivative freezes, and all transient multipolar structure of the infalling plasma redshifts away. The remaining stationary, axisymmetric, asymptotically flat electrovacuum is uniquely the Kerr--Newman geometry, so that the exterior of the compact object is characterised only by its mass $M$, angular momentum $J$ and charge $Q$. The result provides a local, conservation-law-based perspective on the black hole no-hair theorem that is complementary to the classical Israel--Carter-- Robinson theorems and to contemporary gravitational-wave and Event Horizon Telescope tests.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04983",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuanya Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6tqwvf7jxwfmt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04983",
  "fulltext_url": null,
  "id": "6tqwvf7jxwfmt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04983",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "3103|Astrophysical Phenomena and Observations"
    ]
  ],
  "openalex": "W7220722003",
  "pdf_url": "https://arxiv.org/pdf/2610.04983",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6tqwvf7jxwfmt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04983",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04983"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Spacetime-Diffeomorphic Approach to Magnetohydrodynamics around Black Holes: Dilation Covariance, Linearization,and the No-Hair Limit",
  "title_text": "A Spacetime-Diffeomorphic Approach to Magnetohydrodynamics around Black Holes: Dilation Covariance, Linearization,and the No-Hair Limit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/6tqwvf7jxwfmt",
  "venue": "arXiv",
  "versions": []
}