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

TL;DR

This paper investigates the double shadow phenomenon of a 4D Einstein-Gauss-Bonnet black hole caused by photon polarization effects, and explores the connection between quasinormal modes and shadow radius.

Contribution

It introduces the concept of double shadows due to Weyl tensor coupling and analyzes how coupling parameters influence black hole shadows and quasinormal modes.

Findings

Photon polarization leads to double shadows.

The real part of QNMs is inversely proportional to shadow radius in the eikonal limit.

Coupling parameters significantly affect shadow size and QNM frequencies.

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 $\lambda$, 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.