{
  "abstract": "We analyze circular-orbit stability, epicyclic resonances, relativistic precession, and quasi-periodic-oscillation (QPO) constraints in the constant-curvature vacuum sector of metric $f(R)$ gravity. The Schwarzschild--(anti-)de~Sitter and Kerr--(anti-)de~Sitter backgrounds are characterized by curvature $R_0$ satisfying the algebraic trace equation. We derive stationary-coordinate-time orbital and epicyclic frequencies and determine stable timelike circular-orbit domains. Positive curvature confines stable motion between innermost and outermost stable circular orbits, which merge at a critical curvature, and permits two resonance radii for suitable frequency ratios. Negative curvature allows stable motion to arbitrarily large radii, with $Ω_θ/Ω_r\\rightarrow1/2$, compared with unity in the asymptotically flat limit. We determine the $3{:}2$, $2{:}1$, and $3{:}1$ resonance branches and signed nodal precession, recovering the Lense--Thirring limit. We also evaluate angular-momentum-weighted rigid-flow precession and viscous alignment, with the outermost stable orbit bounding positive-curvature flows. A Bayesian Markov chain Monte Carlo analysis combining the simultaneous GRO J1655--40 QPO triplet with an independent dynamical-mass measurement yields $R_0M^2=-5.57^{+12.94}_{-16.15}\\times10^{-4}$ at $68\\%$ credibility, conditional on the geodesic relativistic-precession prescription and adopted time normalization. Kerr remains allowed, with negligible fit improvement from nonzero curvature. Doubling the mass uncertainty broadens the curvature interval by approximately $2.1$; removing the mass likelihood reveals an extended, prior-dependent degeneracy. This is therefore a joint QPO and dynamical-mass constraint, with no significant evidence for departure from Kerr.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37962",
  "author_total": 4,
  "authors": [
    {
      "name": "Kourosh Nozari"
    },
    {
      "name": "Sara Saghafi"
    },
    {
      "name": "Khadijeh Salahshour"
    },
    {
      "name": "Moisés Bravo-Gaete"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27h3enxm6z97y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37962",
  "fulltext_url": null,
  "id": "27h3enxm6z97y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37962",
  "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|Astrophysical Phenomena and Observations"
    ]
  ],
  "openalex": "W7214896139",
  "pdf_url": "https://arxiv.org/pdf/2609.37962",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/27h3enxm6z97y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.37962",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37962"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Orbital stability, relativistic precession, and QPO constraints for constant-curvature black holes in $f(R)$ gravity",
  "title_text": "Orbital stability, relativistic precession, and QPO constraints for constant-curvature black holes in f(R) gravity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/27h3enxm6z97y",
  "venue": "arXiv",
  "versions": []
}