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 $$\alpha $$α and another branch, nonperturbative in $$\alpha $$α. 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 $$\alpha $$α 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.

The correspondence between shadow and test field in a four-dimensional charged Einstein–Gauss–Bonnet black hole

“…This four-dimensional Einstein-Gauss-Bonnet gravity theory was further improved and a consistent theory was proposed in [58]. The generalization to other black hole solutions are referred to [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78].…”

Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity

“…Interestingly, the solution of the same form has been presented in the conformal anomaly inspired gravity [40,41]. Along this line, the Einstein-Gauss-Bonnet gravity in the 4D spacetime has been explored extensively on various aspects, including the exact solutions [42][43][44][45][46][47][48][49][50][51][52][53][54][55], the quasinormal modes and stability [56][57][58][59][60][61][62][63][64][65][66][67], the observable shadows [68][69][70][71][72][73], the geodesics and gravitational lensing [74][75][76][77][78], and the thermodynamics and cosmic censorship conjecture [79][80][81][82][83][84][85][86].…”

Anomalous decay rate of quasinormal modes in Schwarzschild-dS and Schwarzschild-AdS black holes

“…However, the cosmological constant is introducing another scale and it is interesting to see what is the effect on the anomalous behaviour of the competition of the two scales for both positive and negative cosmological constant. We carry out this study by using the pseudospectral Chebyshev method [26] which is an effective method to find high overtone modes [27][28][29][30][31].…”