Modifications to general relativity lead to effects in the spectrum of quasinormal modes of black holes. In this paper, we develop a parametrized formalism to describe deviations from general relativity in the Teukolsky equation, which governs linear perturbations of spinning black holes. We do this by introducing a correction to the effective potential of the Teukolsky equation in the form of a 1/𝑟 expansion controlled by free parameters. The method assumes that a small deviation in the effective potential induces a small modification in the spectrum of modes and in the angular separation constants. We isolate and compute the universal linear contribution to the quasinormal mode frequencies and separation constants in a set of coefficients and test them against known examples in the literature (massive scalar field, Dudley-Finley equation and higher-derivative gravity). We make the coefficients publicly available for relevant overtone, angular momentum, and azimuthal numbers of modes and different values of the black hole spin.

中文翻译：

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用于修正 Teukolsky 方程的参数化准正态框架


对广义相对论的修改会导致黑洞准正态模式光谱的影响。在本文中，我们开发了一种参数化形式主义来描述与 Teukolsky 方程中广义相对论的偏差，该方程控制旋转黑洞的线性扰动。我们通过引入对 Teukolsky 方程的有效势的校正来实现这一点，其形式是由自由参数控制的 1/r 膨胀。该方法假设有效电位的微小偏差会导致模式谱和角度分离常数的微小变化。我们在一组系数中分离并计算准法态模态频率和分离常数的普遍线性贡献，并根据文献中的已知示例（大质量标量场、Dudley-Finley 方程和高导数引力）对其进行测试。我们公开了相关泛音、角动量和模式的方位数以及黑洞自旋的不同值的系数。