Quasinormal modes of Reissner-Nordström black hole from bound state spectrum

Abstract

We apply a newly proposed bound state method to revisit the computation of gravitational and electromagnetic quasinormal modes (QNMs) for Reissner-Nordström black holes (RNBHs). It is found that the method yields QNM frequencies of high accuracy for low-lying modes with overtones $n\leq3$. The accuracy degrades for higher overtones, however, a homotopy deformation to the potential enables us to compute more high overtone modes reliably. It is known that the continued fraction method for computing QNMs of extremal RNBHs differs significantly from that used for nonextremal ones. In contrast, the bound state method demonstrates advantage of simplicity: one only need to account for the definition of tortoise coordinate in the extremal case, and the rest of the computational procedure remains exactly the same as that for the nonextremal case.