Pole-skipping, algebraically special points and absorption of Schwarzschild black holes in four dimensions

我目前的研究重点是四维高度对称空间的引力扰动的基本结构。更具体地说，它通过所谓的达布变换关注引力扰动的独立通道之间的对称性。通过它们，摄动方程可以被编码成所谓的代数特解。与此相关的是，我研究了在视界施加进入边界条件并不能唯一地决定摄动方程解的点，称为跳极点。我指出了它们可能的物理含义。此外，我试图在全息摄影的背景下应用达布形式主义，它将呈现剪切和声音相关器之间的二元性。

My current research is focused on the underlying structure of gravitational perturbations of highly symmetric spaces in four dimensions. More specifically, it is focused on symmetry between the independent channels of gravitational perturbations through the so-called Darboux transformations. Through them the perturbation equations can be encoded in the so-called algebraically special solutions. Related to them, I study points where imposing the ingoing boundary condition at the horizon does not uniquely determine the solution to the perturbation equations, called pole-skipping points. I address their possible physical implications. Moreover, I seek to apply the Darboux formalism in the context of holography where it would present a duality between shear and sound correlators.