Double shadow of a 4D Einstein–Gauss–Bonnet black hole and the connection between them with quasinormal modes

Abstract

In this paper, we 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. Then, we discuss the effect of the coupling parameter [Formula: see text], the polarization of light and the Gauss–Bonnet coupling constant [Formula: see text] on the shadow. Further, we explore the influence of the Gauss–Bonnet coupling constant [Formula: see text] 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 shadow radius of black holes. We find that in the eikonal limit, the real part of QNMs is inversely proportional to the shadow radius under the case of the photons uncoupled to the Weyl tensor.