Bardeen black hole in magnetically charged four-dimensional Einstein-Gauss-Bonnet gravity

Abstract

In this paper, we investigate the shadow radius and quasinormal modes of a fourdimensional magnetically charged Einstein-Gauss-Bonnet Bardeen black hole and point out a simple connection between them in the eikonal limit. By studying a massless scalar field perturbation in this spacetime background and using the sixth-order Wentzel-Kramers-Brillouin (WKB) approximation, we get the quasinormal modes(QNMs) and perform a detailed analysis. It shows that the quasinormal modes are depend on the Gauss-Bonnet coupling constant α and the magnetic charge g. When the value of g increases, the values of the real parts of the QNMs increase and those of the imaginary parts decrease. There is a similar effect on α. We also give a formula of the QNMs and shadow radius in the eikonal limit and check it numerically for the real and imaginary part of it, respectively.