Spin-3/2 fields in $D$-dimensional Schwarzschild black hole space-times

TL;DR

This paper extends the analysis of spin-3/2 fields to D-dimensional Schwarzschild black holes, deriving a gauge-invariant potential and calculating quasi-normal modes and absorption probabilities without relying on the Newman-Penrose formalism.

Contribution

It introduces a method to determine the potential of spin-3/2 fields in D-dimensional black holes using radial symmetry, avoiding complex formalisms.

Findings

Derived a general D-dimensional gauge-invariant potential for spin-3/2 fields.

Calculated quasi-normal modes for spin-3/2 fields in D-dimensional Schwarzschild black holes.

Determined absorption probabilities for these fields.

Abstract

In previous works we have studied spin-3/2 fields near 4-dimensional Schwarzschild black holes. The techniques we developed in that case have now been extended here to show that it is possible to determine the potential of spin-3/2 fields near $D$-dimensional black holes by exploiting the radial symmetry of the system. This removes the need to use the Newman-Penrose formalism, which is difficult to extend to $D$-dimensional space-times. In this paper we will derive a general $D$-dimensional gauge invariant effective potential for spin-3/2 fields near black hole systems. We then use this potential to determine the quasi-normal modes and absorption probabilities of spin-3/2 fields near a $D$-dimensional Schwarzschild black hole.