Gravitational quasinormal modes of static Einstein-Gauss-Bonnet anti-de Sitter black holes

In this paper, we describe quasinormal modes（QNMs） for gravitational perturbations of Einstein-GaussBonnet black holes（BHs） in higher dimensional spacetimes, and derive the corresponding parameters of such black holes in three types of spacetime（flat, de Sitter（d S） and anti-de Sitter（Ad S））. Our attention is concentrated on discussing the（in）stability of Einstein-Gauss-Bonnet Ad S BHs through the temporal evolution of all types of gravitational perturbation fields（tensor, vector and scalar）. It is concluded that the potential functions in vector and scalar gravitational perturbations have negative regions, which suppress quasinormal ringing. Furthermore,the influences of the Gauss-Bonnet coupling parameter α, the number of dimensions n and the angular momentum quantum number l on the Einstein-Gauss-Bonnet Ad S BHs quasinormal spectrum are analyzed. The QNM frequencies have greater oscillation and lower damping rate with the growth of α. This indicates that QNM frequencies become increasingly unstable with large α. Meanwhile, the dynamic evolutions of the perturbation field are compliant with the results of computation from the Horowitz and Hubeny method. Because the number of extra dimensions is connected with the string scale, the relationship between α and properties of Einstein-Gauss-Bonnet Ad S BHs might be beneficial for the exploitation of string theory and extra-dimensional brane worlds.