Quasinormal modes of Rarita-Schwinger field in Reissner-Nordstr\"{o}m black hole spacetimes

TL;DR

This paper investigates the quasinormal modes of Rarita-Schwinger fields around Reissner-Nordström black holes using the Newman-Penrose formalism, revealing how frequencies depend on black hole charge and mode number.

Contribution

It introduces four effective potential expressions for Rarita-Schwinger perturbations and demonstrates their identical quasinormal mode spectra using the WKB approximation.

Findings

Real parts of frequencies increase with black hole charge Q.

Damping rates remain nearly unchanged as charge increases.

Frequency behavior is similar to Dirac perturbations.

Abstract

The Newman-Penrose formalism is used to deal with the quasinormal modes(QNM's) of Rarita-Schwinger perturbations outside a Reissner-Nordstr\"{o}m black hole. We obtain four kinds of possible expressions of effective potentials, which are proved to be of the same spectra of quasinormal mode frequencies. The quasinormal mode frequencies evaluated by the WKB potential approximation show that, similar to those for Dirac perturbations, the real parts of the frequencies increase with the charge $Q$ and decrease with the mode number $n$, while the dampings almost keep unchanged as the charge increases.