{
  "abstract": "A critical scaling exponent of $1/2$ was numerically observed for the Kasner parameter of asymptotically flat scalarized black holes and conjectured to be universal [Phys.\\ Rev.\\ Lett.\\ \\textbf{136}, 251402 (2026)]. In the same static, spherically symmetric Einstein--Maxwell--scalar setting, we show that this exponent is not universal. We develop a rigorous mathematical framework and construct couplings realizing exponents $1/(2m)$ for any integer $m\\ge1$ by tuning higher-order terms at fixed quadratic coupling parameter $μ$. Nonlinear interior collapse produces a spacelike Kasner singularity with $β_{\\rm K}\\propto\\varepsilon^{-1}$, where $\\varepsilon$ is the value of scalar field at the event horizon. An exterior branch satisfying $q/q_\\star-1\\propto\\varepsilon^{2m}$, therefore, yields $β_{\\rm K}\\propto|q/q_\\star-1|^{-1/(2m)}$, where $q$ is the charge-to-mass ratio and $q_\\star$ its critical value. We also determine the prefactor explicitly. This recovers the $1/2$ law and establishes a hierarchy including $1/4$ and $1/6$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35500",
  "author_total": 2,
  "authors": [
    {
      "name": "Chihang He"
    },
    {
      "name": "Chao Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eywycahbbchk9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35500",
  "fulltext_url": null,
  "id": "eywycahbbchk9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35500",
  "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",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7214777898",
  "pdf_url": "https://arxiv.org/pdf/2609.35500",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eywycahbbchk9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.35500",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35500"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Kasner critical scaling in Einstein--Maxwell--scalar black holes with nonlinear collapse and scalarization",
  "title_text": "Kasner critical scaling in Einstein--Maxwell--scalar black holes with nonlinear collapse and scalarization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/eywycahbbchk9",
  "venue": "arXiv",
  "versions": []
}