Quasinormal Modes of Charged Fields in Reissner-Nordstrom Backgrounds by Borel-Pade Summation of Bender-Wu Series

TL;DR

This paper develops a method to compute quasinormal mode frequencies of charged fields in Reissner-Nordstrom black holes using Borel-Pade summation of Bender-Wu series, and compares results with established techniques.

Contribution

It extends the Borel-Pade resummation approach to charged fields in Reissner-Nordstrom backgrounds and analyzes zero-damped modes near extremality.

Findings

Good agreement with Leaver's method for damped modes

Numerical evidence for zero-damped modes near extremality

Method effective for modes with finite imaginary parts

Abstract

We extend recent work of Hatsuda on the computation of quasinormal mode frequencies via analytic continuation of bound state energies and Borel-Pade resummation of the Bender-Wu perturbation series to the case of charged fields in the background of Reissner-Nordstrom black holes. We compare the quasinormal mode frequencies obtained in this manner to calculations using Leaver's method of continued fractions, and find good agreement for damped modes (DMs) with imaginary part remaining finite in the extremal limit. We also present numerical evidence that the frequencies of certain zero-damped modes (ZDMs) with imaginary part tending to zero in the extremal limit can be computed when constructing the Bender-Wu expansion about a peak of the potential inside the outer horizon of the black hole.