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

Understand

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 $\lambda$, the polarization of light and the Gauss-Bonnet coupling constant $\alpha$ on shadow.
• Further we explore the influence of the Gauss-Bonnet coupling constant $\alpha$ 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.