Quasi-normal modes and absorption probabilities of spin-3/2 fields in $D$-dimensional Reissner-Nordstr\"om black hole spacetimes

TL;DR

This paper investigates the quasi-normal modes and absorption probabilities of spin-3/2 fields in higher-dimensional Reissner-Nordström black holes, accounting for electromagnetic interactions and analyzing effects of black hole charge on these properties.

Contribution

It extends the analysis of spin-3/2 fields to charged, higher-dimensional black holes using supercovariant derivatives and derives radial equations for different modes.

Findings

Quasi-normal modes vary with black hole charge.

Absorption probabilities depend on the extremality of the black hole.

Supercovariant derivatives are essential for gauge invariance in charged backgrounds.

Abstract

In this paper we consider spin-3/2 fields in a $D$-dimensional Reissner-Nordstr\"om black hole spacetime. As these spacetimes are not Ricci-flat, it is necessary to modify the covariant derivative to the supercovariant derivative, by including terms related to the background electromagnetic fields, so as to maintain the gauge symmetry. Using this supercovariant derivative we arrive at the corresponding Rarita-Schwinger equation in a charged black hole background. As in our previous works, we exploit the spherically symmetry of the spacetime and use the eigenspinor-vectors on an $N$-sphere to derive the radial equations for both non-transverse-traceless (non-TT) modes and TT modes. We then determine the quasi-normal mode and absorption probabilities of the associated gauge-invariant variables using the WKB approximation and the asymptotic iteration method. We then concentrate on how these quantities change with the charge of the black hole, especially when they reach the extremal limits.