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

我目前的研究集中在四维高度对称空间引力扰动的基本结构上。更具体地说，它通过所谓的达布变换来关注引力扰动的独立通道之间的对称性。通过它们可以将摄动方程编码成所谓的代数特解。与此相关，我研究了在地平线上施加进入边界条件不能唯一确定扰动方程的解的点，称为跳极点。我讨论了它们可能的物理影响。此外，我试图将达布形式主义应用于全息术的背景下，在那里它将呈现剪切相关器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.