Pole-skipping is a generic feature of black hole perturbation theory that amounts to the inability of imposing the ingoing boundary condition at the event horizon at certain points in the Fourier space. As a consequence, various quantities, such as time evolution Green’s functions, take the indeterminate value of “0/0”, which can elucidate some of their structure from horizon analysis alone. A complete classification of all such points in the four dimensional maximally symmetric case will be presented with the aid of the hidden structure of perturbation equations that takes the form of Darboux symmetries. This structure relates the solutions of two independent Schrodinger-type master equations of the perturbation theory. Implications for physical black holes will be discussed, as well as the relation to dual holographic QFTs.

* Mile Vrbica: University of Edinburgh – Scotland.