The Teukolsky equations are currently the leading approach for analysing stability of linear massless fields propagating in rotating black holes. It has recently been shown that the geometry of these equations can be understood in terms of a connection constructed from the conformal and complex structure of Petrov type D spaces. Since the study of linear massless fields by a combination of conformal, complex and spinor methods is a distinctive feature of twistor theory, and since versions of the twistor equation have recently been shown to appear in the Teukolsky equations, this raises the question of whether there are deeper twistor structures underlying this geometry. In this work we show that all these geometric structures can be understood naturally by considering a 2-dimensional twistor manifold, whereas in twistor theory the standard (projective) twistor space is 3-dimensional.

中文翻译：

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二维扭曲流形和 Teukolsky 算子

Teukolsky 方程是目前分析在旋转黑洞中传播的线性无质量场稳定性的主要方法。最近的研究表明，这些方程的几何结构可以根据由彼得罗夫 D 型空间的共形和复杂结构构造的连接来理解。由于通过保形、复数和旋量方法的组合研究线性无质量场是扭曲理论的一个显着特征，而且由于扭曲方程的版本最近被证明出现在 Teukolsky 方程中，这就提出了一个问题：是这种几何结构下更深的扭曲结构。在这项工作中，我们表明通过考虑二维扭曲流形，可以自然地理解所有这些几何结构，