Perturbative and nonperturbative quasinormal modes of 4D Einstein–Gauss–Bonnet black holes

Abstract

We study the propagation of probe scalar fields in the background of 4D Einstein–Gauss–Bonnet black holes with anti-de Sitter (AdS) asymptotics and calculate the quasinormal modes. Mainly, we show that the quasinormal spectrum consists of two different branches, a branch perturbative in the Gauss–Bonnet coupling constant $\alpha$ and another branch, nonperturbative in $\alpha$. The perturbative branch consists of complex quasinormal frequencies that approximate the quasinormal frequencies of the Schwarzschild AdS black hole in the limit of a null coupling constant. On the other hand, the nonperturbative branch consists of purely imaginary frequencies and is characterized by the growth of the imaginary part when $\alpha$ decreases, diverging in the limit of null coupling constant; therefore they do not exist for the Schwarzschild AdS black hole. Also, we find that the imaginary part of the quasinormal frequencies is always negative for both branches; therefore, the propagation of scalar fields is stable in this background.