AI 中文总结
研究黑洞周围颗粒随机动力学，用曲率加权随机游走建模吸积变异性。通过求解福克 - 普朗克方程及模拟轨迹发现相关特性，其谱与观测大致匹配，表明几何漂移对描述随机吸积过程有重要意义。
AI 中文摘要
处于强引力场中的湍流流体中颗粒的随机动力学可表述为黎曼流形上的随机游走。这种曲率加权游走为模拟致密天体吸积的内在变异性提供了框架。通过在黑洞背景下求解相关福克 - 普朗克方程，发现颗粒逃逸概率比平坦空间更高，这是事件视界附近径向单元拉伸的结果。通过模拟大量颗粒轨迹，研究了穿过视界的粒子通量。相对于平坦空间，低频处谱指数更浅，高频处更陡。发现史瓦西加权谱与天鹅座X - 1等系统硬态下低频X射线变异性观测大致匹配，表明几何漂移在描述随机吸积过程中可能很重要。
英文摘要
The stochastic dynamics of a grain embedded within a turbulent fluid subject to strong gravitational fields can be formulated as a random walk on a Riemannian manifold. Such curvature-weighted walks provide a framework to model the intrinsic variability of accretion onto compact objects. By solving the relevant Fokker-Planck equation on a black hole background, we find the counterintuitive result that the escape probability of a grain is actually higher compared to flat space. This is a consequence of the stretching of radial cells near the event horizon: there is a greater spatial volume for the particle to wander through before being captured. By simulating a large number of grain trajectories, initially distributed on concentric shells with a density profile set by the thin-disc structure equations, we also study particle fluxes through the horizon. Shallower spectral indices emerge at low frequencies relative to flat space, primarily due to time dilation, and steeper ones at high frequencies. We find that Schwarzschild-weighted spectra broadly match observations of low-frequency X-ray variability from systems like Cygnus X-1 in their hard state, suggesting that geometric drifts may be important in describing stochastic accretion processes.
Comments12 pages, 9 figures. Accepted for publication in Classical and Quantum Gravity
Journal refClass. Quantum Grav. 43 135032 (2026)
