Validity of the WKB approximation in calculating the asymptotic quasinormal modes of black holes

In this paper, we categorize nonrotating black hole spacetimes based on their pole structure, and in each of these categories we determine whether the WKB approximation is a valid approximation for calculating the asymptotic quasinormal modes. We show that Schwarzschild black holes with the Gauss-Bonnet (G-B) correction belong to the category in which the WKB approximation is invalid for calculating these modes. In this context, we further discuss and clarify some of the ambiguity in the literature surrounding a validity condition provided for the WKB approximation.