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

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.