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.
Highlights
In this work we consider 4D Einstein–Gauss–Bonnet black holes with anti-de Sitter (AdS) asymptotics and we study the propagation of scalar fields in such backgrounds, in order to show the existence of nonperturbative quasinormal modes (QNMs) for this kind of theories
We considered 4D Einstein–Gauss–Bonnet black holes in AdS spacetime as backgrounds and we studied the propagation of probe scalar fields
We found numerically the quasinormal frequencies for different values of the Gauss–Bonnet coupling constant α/R2, the multipole number and the mass of the scalar field m R by using the pseudospectral Chebyshev method
Summary
Following the prescription given in [1] and taking the limit D → 4 it is possible to obtain the exact solution representing the 4D Einstein–Maxwell Gauss–Bonnet black hole [2]: ⎛. Where M is the mass of black hole and Q is its electric charge. On we will consider the uncharged version Q = 0 of the black hole metric:. The black hole horizon rH corresponds to the largest root of f (r ) = 0. The QNMs of scalar perturbations in the background of the metric (4) are given by the scalar field solution of the Klein– Gordon equation,. The effective potential diverges at spatial infinity and it is positive definite everywhere outside the event horizon; see Fig. 2. We will consider as a boundary condition that the scalar field vanishes at the asymptotic region (the Dirichlet boundary condition)
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