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

TL;DR

This paper explores the relationship between shadow radius and quasinormal modes of a magnetically charged Bardeen black hole within four-dimensional Einstein-Gauss-Bonnet gravity, revealing dependencies on specific physical parameters.

Contribution

It establishes a simple connection between shadow radius and quasinormal modes in the eikonal limit for this black hole model, including new formulas and numerical validation.

Findings

Quasinormal modes depend on Gauss-Bonnet coupling and magnetic charge.

Derived formulas relate shadow radius and quasinormal modes in the eikonal limit.

Numerical analysis confirms the theoretical relationships.

Abstract

In this paper, we investigate the shadow radius and quasinormal modes of a four-dimensional 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 and the magnetic charge. 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.