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The WKB approach for finding quasinormal modes of black holes, suggested in[1] by Schutz and Will at the first order and later developed to higher orders[2-4], became popular during the past decades, because, unlike moresophisticated numerical approaches, it is automatic for different effectivepotentials and mostly provides sufficient accuracy. At the same time, theseeming simplicity of the WKB approach resulted in appearance of a big numberof partially misleading papers, where the WKB formula was used beyond its scopeof applicability. Here we review various situations in which the WKB formulacan or cannot bring us to reliable conclusions. As the WKB series convergesonly asymptotically, there is no mathematically strict criterium for evaluationof an error. Therefore, here we are trying to introduce a number of practicalrecipes instead and summarize cases in which higher WKB orders improveaccuracy. We show that averaging of the Pade approximations, suggested first byJ. Matyjasek and M. Opala [4], leads to much higher accuracy of the WKBapproach, estimate the error and present the automatic code [5] which computesquasinormal modes and grey-body factors.

Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations