标题： 缓慢旋转的爱因斯坦-布姆贝黑洞中大质量标量场的准正则模态 显示英文标题

标题： Quasinormal Modes of a Massive Scalar Field in Slowly Rotating Einstein-Bumblebee Black Holes

摘要： 在本研究中，我们考察了黑洞自转、洛伦兹破坏参数以及标量场质量对旋转爱因斯坦-布姆布尔黑洞的准正则模（QNMs）的影响，包括在旋转参数上的二阶展开计算。我们研究了两类洛伦兹破坏的旋转黑洞：一种是通过纽曼-贾尼思算法构建的，另一种是通过级数展开求解场方程得到的。在慢旋转近似框架下，我们推导了带有质量的标量场的主方程，并使用连续分数法和矩阵法数值计算了相应的QNMs频率。数值结果表明，QNMs频率对负的$\ell$变化表现出更高的敏感性，这会减弱场质量参数$\tilde{\mu}$的影响。同时，与另一类黑洞相比，NJA黑洞的频谱“立方体”在$m>0$与$ \ell>0 $的情况下显示出轻微压缩，在$m<0$与$ \ell>0 $的情况下显示出扩张，其中$m$在一阶情况下大约与自转参数成正比，而在二阶情况下出现更丰富的结构和解除简并。 显示英文摘要

摘要： In this study, we examine the impacts of black hole spin, Lorentz-violating parameter, and the scalar field's mass on quasinormal modes (QNMs) of rotating Einstein-Bumblebee black holes, including computations up to the second-order expansion in rotation parameters. We investigate two classes of Lorentz-violating rotating black holes: one constructed via the Newman-Janis algorithm and the other obtained by solving the field equations through a series expansion. Within the slow-rotation approximation framework, we derive the master equations governing a massive scalar field and compute the corresponding QNM frequencies numerically using both the continued fraction method and the matrix method. The numerical results indicate that the QNM frequencies exhibit increased sensitivity to negative $\ell$ variations, which reduces the influence of the field mass parameter $\tilde{\mu}$. Meanwhile, the spectral "cube" of NJA black holes shows slight compression for $m>0$ with $ \ell>0 $ and expansion for $m<0$ with $ \ell>0 $ compared to another black holes, where $m$ is approximately proportional to the spin parameter at first order, while richer structures and lifted degeneracy emerge at second order.