AI 中文总结
研究通过多种方法探究嵌入完美流体暗物质的克尔黑洞中量子改进参数和PFDM参数对光子动力学的影响，发现二者联合效应改变有效势，导致丰富相空间结构，强调其对黑洞附近光子动力学及相关观测的重要作用。
AI 中文摘要
我们使用多种分析方法研究了由完美流体暗物质（PFDM）包围的量子改进旋转黑洞中的非线性光子动力学，包括庞加莱截面、李雅普诺夫指数、柯尔莫哥洛夫 - 西奈（KS）熵和加权伯克霍夫平均（WBA）。特别研究了量子改进参数（\(\tilde{\omega}\)）和PFDM参数（\(\zeta\)）对零测地线运动及圆轨道稳定性的影响。庞加莱截面表明随着这些参数增加，运动从规则转变为混沌，李雅普诺夫指标量化了零圆轨道稳定性，KS熵证实混沌行为随量子和PFDM修正增加，WBA方法区分规则和混沌轨道并绘制相空间结构。结果表明量子引力修正和PFDM的联合效应显著改变了控制光子运动的有效势，导致丰富的混合相空间结构，强调了量子和暗物质在塑造旋转黑洞附近光子动力学中的关键作用及对强场区域黑洞阴影和引力透镜的观测意义。
英文摘要
We study the nonlinear photon dynamics in quantum improved rotating black hole surrounded by perfect fluid dark matter (PFDM) using several methods of analysis, including Poincaré sections, Lyapunov exponents, Kolmogorov-Sinai (KS) entropy and weighted Birkhoff averages (WBA). In particular, we examine the effect of quantum-improved parameter $(\tildeω)$ and PFDM parameter $(ζ)$ on the null geodesic motion hence stability of circular orbit. Poincaré sections illustrate the transition from regular to chaotic motion as these parameters increase, characterized by the deformation and fragmentation of invariant tori and the emergence of scattered chaotic regions in phase space. The stability properties of null circular orbits are quantified through the Lyapunov indicators, revealing that both the quantum improvement parameter and the PFDM parameter enhance the sensitivity of photon trajectories to initial conditions. The KS entropy provides an independent measure of dynamical complexity and confirms the growth of chaotic behavior with increasing quantum and PFDM corrections. Additionally, the WBA method offers a robust quantitative criterion for distinguishing regular and chaotic orbits and allows a detailed mapping of the phase-space structure. The results demonstrate that the combined effects of quantum gravity corrections and PFDM significantly modify the effective potential governing photon motion, leading to a rich mixed phase-space structure with coexisting regular and chaotic regions. These findings underscore the crucial role of quantum and dark matter contributions in shaping photon dynamics near rotating black holes and suggest possible observational implications on black hole shadows and gravitational lensing in strong-field regimes.
Comments16 pages, 12 figures
