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

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.

Figure 1

The behavior of $\mathrm{Re}(\omega )R$ (left panel) and $\mathrm{Im}(\omega )R$ (right panel) versus $\alpha /R^2$ for the perturbative branch in $\alpha$ with $D=5$, $r_H/R=5$, $\lambda =1.5i$ and different values of the mass $m$ and $\alpha$. $mR=0.01$ (blue, upper), $mR=0.1$ (red, middle) and $mR=0.2$ (black, lower).

Figure 2

The behavior of $\mathrm{Re}(\omega )R$ (left panel) and $\mathrm{Im}(\omega )R$ (right panel) versus $\alpha /R^2$ for the perturbative branch in $\alpha$ with $D=5$, $r_H/R=5$ and $mR=0.1$. Blue points for $\lambda =1.5i$ (lower) and red points for $\lambda =2.5i$ (upper).

Figure 3

The behavior of $\mathrm{Re}(\omega )R$ (left panel) and $\mathrm{Im}(\omega )R$ (right panel) versus $\alpha /R^2$ for the perturbative branch in $\alpha$ with $D=5$, $r_H/R=5$ and $mR=0.1$. Blue points for $\lambda =1.5i$ (lower) and red points for $\lambda =2.5i$ (upper).

Figure 4

The behavior of $\mathrm{Re}(\omega )R$ (left panel) and $\mathrm{Im}(\omega )R$ (right panel) for the perturbative branch in $\alpha$ (blue) and for the nonperturbative branch in $\alpha$ (red) with $D=6$, $r_H/R=5$, $\lambda =2i$ and $mR=0.1$. The region $0.42\lesssim \tilde{\alpha }/R^2\lesssim 0.6$ corresponds to (eikonal) gravitational instability [21].