Oscillations of a Black Hole

Abstract
A new analytic method for the determination of quasinormal oscillations of a black hole is presented. It is based on a connection between the quasinormal modes and the bound states of the inverted black-hole potentials. With use of this method, the quasinormal frequencies of a Schwarzschild, a Reissner-Nordström, and a slowly rotating Kerr black hole are determined in the eikonal approximation, Moreover, we provide evidence for the stability of an extreme Kerr black hole.