In the framework of black hole perturbation theory, this work investigates the standing wave solutions in Reissner-Nordtsröm (RN) anti–de Sitter (AdS) spacetimes with a naked singularity. These solutions can be viewed as a specific class of quasinormal modes exhibiting distinct characteristics. The imaginary parts of their frequencies are numerically vanishing, allowing them to persist over an extended period. Besides, these modes are predominantly stationary in terms of the evolution of spacetime waveforms. The numerical calculations are carried out employing the finite difference method, and the quasinormal frequencies extracted by the Prony method are shown to be consistent with those obtained using the matrix method. The obtained waveforms and quasinormal frequencies are shown to be drastically different from those of an extreme RN-AdS black hole. As the quasinormal modes are primarily dissipative, the nondissipative standing waves are attributed to the nature that the singularity can neither be a sink nor a source of the gravitational system.

中文翻译：

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具有裸奇点的扰动反德西特时空中的驻波

在黑洞微扰理论的框架内，这项工作研究了带有裸奇点的 Reissner-Nordtsröm (RN) 反德西特 (AdS) 时空中的驻波解。这些解可以被视为一类特定的准正规模式，表现出不同的特征。它们频率的虚部在数字上消失，使它们能够持续很长一段时间。此外，这些模式在时空波形的演化方面主要是静止的。采用有限差分法进行数值计算，Prony法提取的拟正规频率与矩阵法提取的拟正规频率一致。所获得的波形和准正常频率与极端 RN-AdS 黑洞的波形和准正常频率有很大不同。由于准正则模式主要是耗散的，因此非耗散驻波归因于奇点既不能是引力系统的汇也不能是源的性质。