发表机构
National University of Uzbekistan; Samarqand State Pedagogical Institute; Institute of Fundamental and Applied Research, National Research University TIIAME; Tashkent State Technical University; School of Physics, Harbin Institute of Technology; University of Tashkent for Applied Sciences; Institute of Theoretical Physics, National University of Uzbekistan; New Uzbekistan University; Kimyo International University in Tashkent; University of Economics and Pedagogy; Tashkent International University（乌兹别克斯坦国立大学; 撒马尔罕国立师范学院; 塔什干信息技术与管理系统国立研究大学基础与应用研究所; 塔什干国立技术大学; 哈尔滨工业大学物理学院; 塔什干应用科学大学; 乌兹别克斯坦国立大学理论物理研究所; 新乌兹别克斯坦大学; 塔什干基莫国际大学; 经济与教育学院; 塔什干国际大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究量子涨落修正引力中尘埃场包围的黑洞，发现参数K和α对视界及轨道频率起相反作用，并用三种双峰QPO模型拟合四个源数据，给出K∈(0,0.5)、α∈(0.3,0.6)的约束。
AI 中文摘要
我们研究了量子涨落修正引力中一个被尘埃场包围的静态、球对称黑洞解，其中包含量子涨落参数 $\alpha$ 和尘埃场强度参数 $K$。视界结构揭示这两个参数起相反作用：增强 $K$ 会使内视界和外视界相互靠近，直至合并为一个极端视界，而更大的 $\alpha$ 则恢复史瓦西极限；这一相反的趋向同样延伸到有效势和特征圆轨道半径——最内稳定圆轨道、边际束缚轨道和边际圆轨道——它们随 $K$ 向内移动，随 $\alpha$ 向外移动，也延伸到有质量测试粒子的开普勒频率和径向本轮频率。基于这些频率，我们构建了三种双峰准周期振荡模型——相对论进动、翘曲盘和本轮共振——以及它们的 $3{:}2$、$4{:}3$ 和 $5{:}4$ 共振半径，所有这些都遵循相同的 $K$-$\alpha$ 趋向。通过马尔可夫链蒙特卡洛分析，将三种模型与来自两个恒星质量源（GRO~J1655$-$40、XTE~J1550$-$564）和两个中等质量源（M82~X$-$1、NGC~1313~X$-$1）的双峰准周期振荡数据进行比较，在 $2\sigma$ 水平上给出了最佳拟合约束：所有源和模型的 $K\in(0,0.5)$ 和 $\alpha\in(0.3,0.6)$。
英文摘要
We study a static, spherically symmetric black hole solution surrounded by a dust field within quantum fluctuation modified gravity, in which the quantum-fluctuation parameter $α$ and the dust-field strength parameter $K$. The horizon structure reveals the two parameters acting in opposite directions: strengthening $K$ draws the inner and outer horizons together until they merge into a single extremal horizon, while a larger $α$ restores the Schwarzschild limit; the same opposing trend extends to the effective potential and the characteristic circular-orbit radii -- the innermost stable circular orbit, the marginally bound orbit, and the marginal circular orbit -- which shift inward with $K$ and outward with $α$, and to the Keplerian and radial epicyclic frequencies of massive test particles. From these frequencies we build three twin-peak quasi-periodic oscillation models -- relativistic precession, warped-disk, and epicyclic-resonance -- along with their $3{:}2$, $4{:}3$, and $5{:}4$ resonance radii, all following the same $K$-$α$ trend. Testing all three models against twin-peak QPO data from two stellar-mass (GRO~J1655$-$40, XTE~J1550$-$564) and two intermediate-mass (M82~X$-$1, NGC~1313~X$-$1) sources through a Markov Chain Monte Carlo analysis places best-fit constraints, at the $2σ$ level, of $K\in(0,0.5)$ and $α\in(0.3,0.6)$ across all sources and models.
