发表机构
University of Mazandaran; Universidad Católica del Maule（马赞德兰大学; 马乌莱天主教大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在 $f(R)$ 引力常曲率背景下分析轨道稳定性与进动，结合QPO和动力学质量数据给出曲率约束，未发现偏离Kerr的显著证据。
AI 中文摘要
我们分析了度规 $f(R)$ 引力常曲率真空扇区中的圆轨道稳定性、内共振、相对论进动以及准周期振荡（QPO）约束。Schwarzschild–(反)de Sitter 和 Kerr–(反)de Sitter 背景由满足代数迹方程的曲率 $R_0$ 表征。我们推导了稳态坐标时间下的轨道频率和内频率，并确定了稳定的类时圆轨道区域。正曲率将稳定运动限制在最内和最小稳定圆轨道之间，这些轨道在临界曲率处合并，并允许在合适的频率比下存在两个共振半径。负曲率允许稳定运动延伸到任意大的半径，其中 $\Omega_\theta/\Omega_r\rightarrow1/2$，而在渐近平坦极限中该比值为 1。我们确定了 $3{:}2$、$2{:}1$ 和 $3{:}1$ 共振分支以及带符号的节点进动，恢复了 Lense–Thirring 极限。我们还评估了角动量加权的刚性流进动和黏性对齐，最外层稳定轨道限制了正曲率流。结合 GRO J1655–40 同时出现的 QPO 三重态与独立的动力学质量测量的贝叶斯马尔可夫链蒙特卡罗分析，在 68% 置信度下给出 $R_0M^2=-5.57^{+12.94}_{-16.15}\times10^{-4}$，这取决于测地线相对论进动方案和所采用的时间归一化。Kerr 仍然被允许，非零曲率带来的拟合改进可忽略不计。将质量不确定性加倍会使曲率区间扩大约 2.1 倍；移除质量似然则揭示出扩展的、先验依赖的简并性。因此，这是一个联合的 QPO 和动力学质量约束，没有显著证据表明偏离 Kerr 解。
英文摘要
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.
Comments33 pages, 11 figures, 6 tables
