This note addresses quasinormal mode frequencies of four-dimensional asymptotically de Sitter rotating black holes. The main motivation is that Mathematica 12.1 has implemented a new family of special functions: Heun functions. Using the fact that Teukolsky's equations for Kerr-de Sitter black holes are mapped to Heun's equations, we are able to compute their quasinormal mode frequencies by the Heun function. In this approach, Mathematica normally evaluates these frequencies to arbitrary numerical precision in a few seconds. We further discuss an application to asymptotically flat rotating black holes.

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通过 Heun 函数的 Kerr-de Sitter 黑洞的准正规模式

本笔记涉及四维渐近德西特旋转黑洞的准正规模式频率。主要动机是 Mathematica 12.1 实现了一个新的特殊函数系列：Heun 函数。使用 Kerr-de Sitter 黑洞的 Teukolsky 方程映射到 Heun 方程这一事实，我们能够通过 Heun 函数计算它们的准正规模式频率。在这种方法中，Mathematica 通常会在几秒钟内将这些频率评估为任意数值精度。我们进一步讨论了渐近平坦旋转黑洞的应用。