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In this work, we investigate the relationship between the geometricalproperties, the photon sphere, the shadow, and the eikonal quasinormal modes ofelectrically charged black holes in 4D Einstein-Gauss-Bonnet gravity.Quasinormal modes are complex frequency oscillations that are dependent on thegeometry of spacetime and have significant applications in studying black holeproperties and testing alternative theories of gravity. Here, we focus on theeikonal limit for high frequency quasinormal modes and their connection to theblack holes geometric characteristics. To study the photon sphere, quasinormalmodes, and black hole shadow, we employ various techniques such as the WKBmethod in various orders of approximation, the Poschl-Teller potential method,and Churilova's analytical formulas. Our results indicate that the real part ofthe eikonal quasinormal mode frequencies of test fields are linked to theunstable circular null geodesic and are correlated with the shadow radius foran Charged Einstein-Gauss-Bonnet 4D black hole. Furthermore, we found that thereal part of quasinormal modes, the photon sphere and shadow radius have alower value for charged black holes in 4D Einstein-Gauss-Bonnet gravitycompared to black holes without electric charge and those of static black holesin general relativity. Additionally, we explore various analytical formulas forthe photon spheres and shadows, deducing an Churilova's approximate formula forthe black hole shadow radius of the Charged Einstein-Gauss-Bonnet 4D blackhole, which arises from its connection with the eikonal quasinormal modes.

Eikonal quasinormal modes, photon sphere and shadow of a charged black hole in the 4D Einstein-Gauss-Bonnet gravity