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

TL;DR

This paper explores the relationship between black hole shadows and quasinormal modes in a four-dimensional charged Einstein-Gauss-Bonnet black hole, revealing how the Gauss-Bonnet coupling influences these properties and their correspondence.

Contribution

It demonstrates the connection between shadow radius and quasinormal modes in a four-dimensional Einstein-Gauss-Bonnet black hole, highlighting the effects of the Gauss-Bonnet coupling constant.

Findings

Quasinormal mode frequencies increase with the Gauss-Bonnet coupling.

Shadow and photon sphere radii increase as the Gauss-Bonnet coupling decreases.

Higher multiple numbers enhance the correspondence between quasinormal modes and shadow properties.

Abstract

In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a four-dimensional charged Einstein-Gauss-Bonnet black hole. The perturbation of a massless scalar field in the black hole's background is adopted. The quasinormal modes are gotten by the $6th$ order WKB approximation approach and shadow radius, respectively. When the value of the Gauss-Bonnet coupling constant increase, the values of the real parts of the quasinormal modes increase and those of the imaginary parts decrease. The coincidence degrees of quasinormal modes derived by the two approaches increases with the increase of the values of the Gauss-Bonnet coupling constant and multiple number. It shows the correspondence between the shadow and test field in the four-dimensional Einstein-Gauss-Bonnet-Maxwell gravity. The radii of the photon sphere and shadow increase with the decrease of the Gauss-Bonnet coupling constant.