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In this paper, we investigate the shadow radius and quasinormal modes of afour-dimensional magnetically charged Einstein-Gauss-Bonnet Bardeen black holeand point out a simple connection between them in the eikonal limit. Bystudying a massless scalar field perturbation in this spacetime background andusing the sixth-order Wentzel-Kramers-Brillouin(WKB) approximation, we get thequasinormal modes(QNMs) and perform a detailed analysis. It shows that thequasinormal modes are depend on the Gauss-Bonnet coupling constant and themagnetic charge. We also give a formula of the QNMs and shadow radius in theeikonal limit and check it numerically for the real and imaginary part of it,respectively.

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