Validity of the WKB Approximation in Calculating the Asymptotic Quasinormal Modes of Black Holes

TL;DR

This paper evaluates the validity of the WKB approximation in calculating asymptotic quasinormal modes of non-rotating black holes, revealing its limitations for certain black hole categories like Schwarzschild with Gauss-Bonnet corrections.

Contribution

It categorizes black hole spacetimes based on pole structure and clarifies the conditions under which the WKB approximation is valid or invalid for quasinormal mode calculations.

Findings

WKB approximation is invalid for Schwarzschild black holes with Gauss-Bonnet corrections.

Black hole categories are distinguished by their pole structures.

Clarifies ambiguities in existing validity criteria for the WKB approximation.

Abstract

In this paper, we categorize non-rotating 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 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 the validity conditions provided for the WKB approximation.