In the study of perturbations around black hole configurations, whether an external source can influence the perturbation behavior is an interesting topic to investigate. When the source acts as an initial pulse, it is intuitively acceptable that the existing quasinormal frequencies will remain unchanged. However, the confirmation of such an intuition is not trivial for the rotating black hole, since the eigenvalues in the radial and angular parts of the master equations are coupled. We show that for the rotating black holes, a moderate source term in the master equation in the Laplace s-domain does not modify the quasinormal modes. Furthermore, we generalize our discussions to the case where the external source serves as a driving force. Different from an initial pulse, an external source may further drive the system to experience new perturbation modes. To be specific, novel dissipative singularities might be brought into existence and enrich the pole structure. This is a physically relevant scenario, due to its possible implication in modified gravity. Our arguments are based on exploring the pole structure of the solution in the Laplace s-domain with the presence of the external source. The analytical analyses are verified numerically by solving the inhomogeneous differential equation and extracting the dominant complex frequencies by employing the Prony method.

在研究黑洞结构周围的扰动时，外部源是否可以影响扰动行为是一个有趣的研究话题。当信号源充当初始脉冲时，现有准准频率将保持不变，这在直觉上是可以接受的。但是，对于直觉的旋转黑洞来说，这种直觉的确认并非无关紧要，因为主方程的径向和角度部分的特征值是耦合的。我们表明，对于旋转的黑洞，拉普拉斯s域主方程中的中度源项不会修改拟正态模。此外，我们将讨论归纳为外部来源作为驱动力的情况。与初始脉冲不同，外部源可能进一步驱动系统体验新的扰动模式。具体而言，可能会出现新颖的耗散奇点并丰富极点结构。这是一种与物理相关的方案，因为它可能涉及修改后的重力。我们的论据基于在存在外部源的情况下探索Laplace s域中解的极结构。通过求解非齐次微分方程并采用Prony方法提取主导复频，对分析进行了数值验证。我们的论据基于在存在外部源的情况下探索Laplace s域中解的极结构。通过求解非齐次微分方程并采用Prony方法提取主导复频，对分析进行了数值验证。我们的论据基于在存在外部源的情况下探索Laplace s域中解的极结构。通过求解非齐次微分方程并采用Prony方法提取主导复频，对分析进行了数值验证。