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We often encounter a situation where linear wave equations around a black hole solution can be regarded as continuous deformations of simpler ones, or modifications from the general relativity case by continuous parameters. We develop a general framework to compute high-order perturbative corrections to quasinormal mode frequencies in such deformed problems. Our method has many applications, and it allows us to compute numerical values of the high-order corrections very accurately. For several examples, we perform this computation explicitly and discuss analytic properties of the quasinormal mode frequencies for deformation parameters.
Hatsuda et al. (Mon,) studied this question.