The frequencies of low-lying normal modes of Schwarzschild and Kerr black holes due to massive scalar perturbations are calculated using a higher-order WKB approximation. In the Schwarzschild case, for a range of scalar-field angular momenta, it is found that when the mass of the scalar field increases, the oscillation frequency increases, while the damping decreases. The convergence of the approximation is studied as a function of the mass. For the Kerr case, the same general variation with the mass of the field is found.
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Simone et al. (1992) studied this question.
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