Perturbative and nonperturbative fermionic quasinormal modes of Einstein-Gauss-Bonnet-AdS black holes

TL;DR

This paper investigates fermionic quasinormal modes in Gauss-Bonnet-AdS black holes, revealing both perturbative and nonperturbative frequency branches, with nonperturbative modes acquiring a real part and confirming black hole stability.

Contribution

It provides the first analysis of fermionic quasinormal modes showing nonperturbative modes with real parts, extending previous scalar and gravitational studies to fermionic fields.

Findings

Two frequency branches identified: perturbative and nonperturbative.

Nonperturbative modes have non-zero real parts for fermions.

Black holes are stable against fermionic perturbations.

Abstract

In this work, we present the quasinormal modes of a fermionic field in the background of Gauss-Bonnet-AdS black holes. We find exact solutions for $D=5$ at the fixed value $\alpha=R^2/2$ of the Gauss--Bonnet coupling constant, with $R$ denoting the AdS radius, and we find numerical solutions for some range of values of the coupling constant $\alpha$ and $D=5, 6$. Mainly, we find two branches of quasinormal frequencies, a branch perturbative in the Gauss-Bonnet coupling constant $\alpha$, and another branch nonperturbative in $\alpha$. The phenomena of nonperturbative modes, which seem to be quite general in theories with higher curvature corrections, have been obtained in the spectrum of gravitational field perturbations and scalar field perturbations in previous works. We show that it also arises for fermionic field perturbations and therefore seems to be independent of the spin of the field under consideration. However, in contrast to gravitational and scalar field perturbations, where the nonperturbative modes are purely imaginary, we find that for fermionic field perturbations the nonperturbative modes acquire a real part. We find that the imaginary part of the quasinormal frequencies is always negative in both branches; therefore, the spherical Gauss-Bonnet-AdS black holes are stable against fermionic field perturbations.