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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-Nordstr\"om, 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.
Ferrari et al. (1984) studied this question.