Double shadow of a 4D Einstein-Gauss-Bonnet black hole and their connection between with quasinormal modes

Abstract

In this paper, we firstly study the shadow of a 4D Einstein-Gauss-Bonnet black hole as photons couple to the Weyl tensor and find that the propagation of light depends on its polarization which leads to the existence of a double shadow. Further, we discuss the effect of the coupling parameter λ, the polarization of light and the Gauss-Bonnet coupling constant α on shadow. Then we explore the influence of the Gauss-Bonnet coupling constant α on the quasinormal modes (QNMs) of massless scalar field and investigate the connection between the real part of QNMs in the eikonal limit and the modified shadow radius of black holes. We find that in the eikonal limit the real part of QNMs is inversely proportional to the shadow radius, which is also applicable in the case of the photons coupled to the Weyl tensor.