{
  "abstract": "We derive an exact radial monotonicity law for static, spherically symmetric spacetimes in metric \\(f(R)\\) gravity. For \\(ds^2=A(r)dt^2-dr^2/B(r)-r^2dΩ^2\\), the matter contribution and the scalaron Hessian combine into an effective radial-convergence numerator that fixes the derivative of \\(\\Q=B/A\\). On every connected static interval with \\(A>0\\), \\(B>0\\), and \\(f_R\\equiv df/dR>0\\), its sign therefore determines the monotonicity of \\(\\Q\\). The integrated identity retains the finite, generally nonzero value of \\(B/A\\) at a regular nondegenerate Killing horizon; consequently, a fixed-sign convergence condition orders the horizon endpoint ratios rather than excluding two horizons. A zero-integral obstruction arises for equal endpoint values, including boundaries where \\(B\\to0\\) while \\(A\\) remains finite and nonzero. Saturation is equivalent to \\(B/A=\\mathrm{const}\\), and in vacuum requires a scalaron profile linear in the areal radius. We illustrate the strict non-saturated branch, within the General-Relativity sector, using the exact constant-density stellar interior, and apply the equality and consistency diagnostics to the constant-\\(X\\) and power-law solutions of Multamäki and Vilja. In particular, in the Schwarzschild--de Sitter two-horizon parameter range, one constant-\\(X\\) solution crosses \\(f_R=0\\) inside the complete static patch, while a direct substitution into the original radial equation exposes an unresolved exponent mismatch in the displayed power-law family. The results provide a model-independent static-sector diagnostic and a precise starting point for a future horizon-regular treatment of black-hole interiors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phys. Rev. D 114, 064088 (2026)",
  "arxiv": "2608.08818",
  "author_total": 4,
  "authors": [
    {
      "name": "Maickol Muñoz-Palma"
    },
    {
      "name": "Francisco S. N. Lobo"
    },
    {
      "name": "Jean Báez Cuevas"
    },
    {
      "name": "Francisco Tello-Ortiz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cshhbfp8fzbtn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.08818",
  "fulltext_url": null,
  "id": "cshhbfp8fzbtn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.08818",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.08818",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cshhbfp8fzbtn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2608.08818",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.08818"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Scalaron-modified null focusing and radial monotonicity in static f(R) gravity",
  "title_text": "Scalaron-modified null focusing and radial monotonicity in static f(R) gravity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/cshhbfp8fzbtn",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/hnw1-gl3z",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}