{
  "abstract": "Quadratic $f(R)$ gravity carries a massive scalar degree of freedom, the scalaron, whose finite range $λ$ screens its influence on the geometry outside a compact object. We show that this screening severs the exterior of a black hole from that of a neutron star of the same mass. Correction to the Schwarzschild metric is Yukawa-suppressed, falling as $e^{-r/λ}$ in the coupling, and is thus invisible to any expansion in powers of that coupling; the exterior is moreover intrinsically isotropic, so that inverting the temporal potential alone, as one does for single-potential solutions, fails to solve the field equations. Applying the Gibbons & Werner method of the Gauss-Bonnet theorem to this geometry, we find the leading deflection angle to be exactly the general-relativistic, ($b$: impact parameter), scalaron contributions cancelling identically in the combination that bends light. First correction carries the unfamiliar signature $λ^{-1/2}b^{-3/2}e^{-b/λ}$, screened beyond the scalaron range and confirmed against direct quadrature to around 20% at $b=4λ$, improving to 7% at $b=12λ$. What survives is the ingredients that deliver it, namely, non-analyticity in the coupling, the intrinsically isotropic gauge, the closed-form screened correction and the pressure-weighted scalar charge, are obtained within a single, self-consistent derivation here. A static black hole carries no scalar hair, and lenses precisely as general relativity requires; a neutron star acquires a scalar charge weighted by the pressure supporting it against collapse, and does not. Weak lensing therefore closes as a discriminant of the theory, whilst the horizon, as against a material surface, remains one in principle. The observational advantage lies in the strong-field imaging of the photon sphere, and in the stellar interior, where the scalar charge is fixed by the equation of state.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04419",
  "author_total": 2,
  "authors": [
    {
      "name": "Yashmitha Kumaran"
    },
    {
      "name": "Ilídio Lopes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bj8f9mzr93xd7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04419",
  "fulltext_url": null,
  "id": "bj8f9mzr93xd7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04419",
  "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|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7211881346",
  "pdf_url": "https://arxiv.org/pdf/2609.04419",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bj8f9mzr93xd7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2609.04419",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04419"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Screened Scalar Hair and the Weak-Lensing Separation of Black Holes from Neutron Stars in Quadratic $f(R)$ Gravity",
  "title_text": "Screened Scalar Hair and the Weak-Lensing Separation of Black Holes from Neutron Stars in Quadratic f(R) Gravity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/bj8f9mzr93xd7",
  "venue": "arXiv",
  "versions": []
}