# Master equations and Quasi-normal modes of spin-3/2 fields in Schwarzschild (A)dS black hole spacetimes

## TL;DR

This paper studies the behavior of spin-3/2 fields in Schwarzschild (A)dS black hole spacetimes, deriving master equations and calculating quasi-normal modes, highlighting differences caused by the cosmological constant.

## Contribution

It introduces modified supercovariant derivatives for spin-3/2 fields in (A)dS spacetimes and derives master radial equations with energy-dependent potentials.

## Key findings

- Imaginary parts of potentials vanish in AdS cases due to negative cosmological constant.
- Quasi-normal modes are computed using the Horowitz-Hubeny method.
- Effective potentials include explicit imaginary components in general.

## Abstract

In this work we consider spin-3/2 fields in Schwarzschild (A)dS black hole spacetimes. As this spacetime is different from the Ricci-flat cases, it is necessary to modify the covariant derivative to the supercovariant derivative in order to maintain the gauge symmetry, as noted in our earlier works, where this is done here by including terms related to the cosmological constant. Together with the eigenmodes for spin-3/2 fields on an $n$-sphere, we derive the master radial equations, which have effective potentials that in general include an explicitly imaginary part and energy dependence. We found that for the asymptotically AdS cases, the explicit imaginary dependence automatically disappears, because of the negative cosmological constant. We take this case as an example and obtain the quasi-normal modes by using the Horowitz-Hubeny method [6].