Bouncing and QNM convergence in Kerr

Abstract

We show that the convergence region of the QNM representation of the retarded Green's function of the Kerr spacetime is set by complex-time bouncing singularities, as in our previous work for the Schwarzschild case. The main difference between Kerr and Schwarzschild is that there are two distinct QNM families, prolate and oblate, which have different convergence regions. We provide explicit analytical formulae for the bounce radii and corresponding convergence regions in Boyer-Lindquist coordinates. We also provide an analysis of convergence in the Reissner-Nordström spacetime.