Quasi-normal modes of spin-3/2 fields in $D$-dimensional Reissner-Nordstr\"om black hole spacetimes using the continued fraction method

TL;DR

This paper investigates the calculation of quasi-normal modes of spin-3/2 fields in higher-dimensional Reissner-Nordström black hole spacetimes, focusing on the challenges faced by existing methods and exploring the continued fraction method as an alternative.

Contribution

It introduces the application of the continued fraction method to compute quasi-normal modes of spin-3/2 fields, addressing limitations of previous approaches like WKB and AIM in complex potentials.

Findings

Effective potential develops multiple maxima in higher dimensions.

WKB and AIM methods face difficulties with complex potential shapes.

Continued fraction method offers a promising alternative for these calculations.

Abstract

In a recent paper we calculated the field equations of spin-3/2 fields in a $D$-dimensional Reissner-Nordstr\"om black hole spacetime whilst maintaining the gauge symmetry of the Rarita-Schwinger equation. We were also able to determine the quasi-normal modes of the associated gauge invariant variables using the WKB approximation and the asymptotic iteration method (AIM). However, it was found that for higher dimension, and especially for the near extremal cases, the effective potential developed another maximum. The shape of the potential posed difficulties for the WKB approximations, as well as the AIM. As such, in this proceedings we would like to explore the connection between the AIM and the continued fraction method, and determine a possible reason for the difficulty in calculating the quasi-normal modes for spin-3/2 fields in this spacetime.