Orbital stability, relativistic precession, and QPO constraints for constant-curvature black holes in f(R) gravity
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 R0 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 Ωθ/Ωr→1/2, 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 R0M2=−5.57+12.94−16.15×10−4 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.
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BibTeX
@misc{nozari2026orbital,
title = {{Orbital stability, relativistic precession, and QPO constraints for constant-curvature black holes in $f(R)$ gravity}},
author = {Kourosh Nozari and Sara Saghafi and Khadijeh Salahshour and Moisés Bravo-Gaete},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37962},
eprint = {2609.37962},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37962},
}
RIS
TY - UNPB
TI - Orbital stability, relativistic precession, and QPO constraints for constant-curvature black holes in f(R) gravity
AU - Kourosh Nozari
AU - Sara Saghafi
AU - Khadijeh Salahshour
AU - Moisés Bravo-Gaete
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37962
UR - https://arxiv.org/abs/2609.37962
AB - 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→1/2, 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_−16.15×10^−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.
ER -