AI 中文总结
研究围绕旋转坍缩物体的薄粘性吸积盘倾斜动力学，通过在全克尔时空推导稳态翘曲盘方程，解析得到径向倾斜剖面，数值解有偏差，发现克尔裸奇点有独特内驼峰特征，其或影响对X射线等特征解释及物体性质推断。
AI 中文摘要
我们在全克尔时空中推导了一个稳态翘曲盘方程，以研究围绕旋转坍缩物体的薄粘性吸积盘的倾斜动力学。该公式基于普林格尔框架，对克尔参数\(a\)的所有值均有效，涵盖克尔黑洞（\(0 < a \le 1\)）和克尔裸奇点（\(a > 1\)）。通过纳入精确的开普勒和楞次 - Thirring进动频率，我们解析得到了盘的径向倾斜剖面，无需调用慢旋转或弱场近似。在实际边界条件下得到的方程数值解显示，与慢旋转近似有显著偏差，特别是在相对论效应主导的内盘。在扩散区域，我们发现对于克尔裸奇点，倾斜剖面在特定角动量消失的半径附近呈现出明显的内驼峰——这是克尔黑洞所没有的特征。考虑内盘倾斜可能会显著影响对观测到的X射线光谱、时间和偏振特征的解释，这些对于探测强引力区域和推断中心物体的自旋至关重要。虽然仅这种明显的驼峰特征不能唯一区分克尔黑洞和克尔裸奇点，但结合对盘区域的限制进行解释可能为吸积坍缩物体的性质提供潜在的观测依据。
英文摘要
We derive a steady-state warped-disk equation in the full Kerr spacetime to study the tilt dynamics of a thin, viscous accretion disk around a spinning collapsed object. The formulation, based on Pringle's framework, remains valid for all values of the Kerr parameter $a$, thereby encompassing both Kerr black holes (BHs; $0 < a \le 1$) and Kerr naked singularities ($a > 1$). By incorporating the exact Keplerian and Lense-Thirring precession frequencies, we analytically obtain the radial tilt equations of the disk without invoking slow-spin or weak-field approximations. Numerical solutions of the resulting equations, obtained under realistic boundary conditions, reveal significant deviations from slow-spin approximations, particularly in the inner disk where the relativistic effects dominate. In the diffusive regime, we find that for Kerr naked singularities the tilt profile exhibits distinct inner hump(s) near the radius where the specific angular momentum vanishes -- a feature absent for Kerr BHs. Consideration of a tilt in the inner disk could significantly influence the interpretations from observed X-ray spectral, timing, and polarization features, which are crucial to probe the strong gravity regime and to infer the spin of the central object. While such a distinct hump feature alone does not uniquely distinguish Kerr BHs from Kerr naked singularities, their interpretation in conjunction with constraints on the disk regime may provide a potential observational handle on the nature of the accreting collapsed object.
Comments25 pages, 17 figures, 2 tables, matches published version
Journal refPhys. Rev. D 114, 043004 (2026)
