An efficient higher-order WKB code for quasinormal modes and greybody factors

TL;DR

This paper introduces an optimized higher-order WKB code for calculating quasinormal modes and greybody factors, significantly reducing computation time while maintaining accuracy, especially for complex potentials.

Contribution

The authors present an improved WKB code that expands the potential in a Taylor series, greatly enhancing computational efficiency without sacrificing precision.

Findings

Speed gain of several orders of magnitude for complex potentials

Maintains accuracy of higher-order WKB calculations

Applicable to a wide range of potential functions

Abstract

The higher-order WKB Mathematica code for computing quasinormal modes, whose accuracy was significantly enhanced through extensions to higher orders and, in particular, through the use of Pad\'e resummation, has been widely employed in numerous studies over the past several years. In this work, we present an updated and optimized version of the code. The main improvement consists in expanding the effective potential in a Taylor series around its maximum, rather than evaluating the full analytic expression of the WKB formula for each specific potential. This modification leads to a substantial reduction in computation time. In cases where the effective potential is complicated and involves non-rational functions, the speed gain can reach several orders of magnitude, while preserving the accuracy of the method.