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A complex matrix WKB approach is applied to study the black hole normal modes and quasibound states problems. In contrast to the standard WKB scheme no asymptotic expansions are used at any stage of the calculations. New quantization formulae are derived which allow for subsequent perturbative calculations to be made in terms of convergent expansions with controlled accuracy. Earlier WKB results are obtained in the lower order approximations of the present approach.
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Gal’tsov et al. (1992) studied this question.
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