AI 中文总结
研究等离子体环境对含拓扑缺陷黑洞光学及微扰性质的影响，通过建立对应关系、推导有效势等方法分析标量和电磁扰动，揭示了等离子体对黑洞相关频率及状态的影响规律。
AI 中文摘要
我们研究了等离子体环境对具有以参数\(k\)为特征的拓扑缺陷的黑洞的光学和微扰性质的影响。首先在几何光学极限下建立了准正则模（QNM）频率实部与黑洞阴影半径之间的直接对应关系。然后表明与光子球相关的李雅普诺夫指数仅对等离子体频率有微弱依赖，随拓扑缺陷参数\(k\)增加单调减小。接着通过推导有效势并使用三阶和六阶WKB近似计算QNM谱来分析大质量标量场微扰。结果表明等离子体的存在会引起模式振荡频率和阻尼率的变化，\(k\)值越大系统地抑制QNM频率的实部。在所考虑的等离子体模型中，非奇异等温球（NSIS）剖面通常产生比奇异等温球（SIS）和均匀情况略高的振荡频率。最后推导了冷、无磁化等离子体中电磁扰动的动力学方程，证明轴向和极向扇区解耦。在轴向扇区，等离子体频率作为有效质量项进入，从而仅在均匀等离子体且等离子体频率低于取决于拓扑缺陷参数\(k\)和多极指数\(l\)的临界阈值时允许准束缚态的存在。
英文摘要
We investigated the influence of a plasma environment on the optical and perturbative properties of a black hole with a topological defect, characterized by the parameter \(k\). We first established a straightforward correspondence between the real part of the quasinormal-mode (QNM) frequencies in the eikonal limit and the black-hole shadow radius. We then demonstrated that the Lyapunov exponent associated with the photon sphere exhibits only a weak dependence on the plasma frequency, while it monotonically decreases as the topological-defect parameter \(k\) increases. Subsequently, we analyzed massive scalar-field perturbations by deriving the associated effective potential and computing the QNM spectrum using the third- and sixth-order WKB approximations for both homogeneous and radially inhomogeneous plasma configurations, including the singular isothermal sphere (SIS) and non-singular isothermal sphere (NSIS) density profiles. Our results show that the presence of plasma induces shifts in both the oscillation frequencies and the damping rates of the modes, and that larger values of \(k\) systematically suppress the real part of the QNM frequencies. Among the plasma models considered, the NSIS profile generally yields slightly higher oscillation frequencies than both the SIS and homogeneous cases. Finally, we derived the dynamical equations governing electromagnetic perturbations in a cold, unmagnetized plasma and demonstrated that the axial and polar sectors decouple. In the axial sector, the plasma frequency enters as an effective mass term, thereby permitting the existence of quasi-bound states only in the case of a homogeneous plasma and only when the plasma frequency lies below a critical threshold that depends on the topological-defect parameter \(k\) and the multipole index \(l\).
Comments16 pages, 8 figures, 4 tables
