Eikonal Quasinormal Modes, Photon Sphere and Shadow of a Charged Black Hole in the 4D Einstein-Gauss-Bonnet Gravity

Abstract

In this work, we investigate the relationship between the geometrical properties, the photon sphere, the shadow, and the eikonal quasinormal modes of electrically charged black holes in 4D Einstein-Gauss-Bonnet gravity. Quasinormal modes are complex frequency oscillations that are dependent on the geometry of spacetime and have significant applications in studying black hole properties and testing alternative theories of gravity. Here, we focus on the eikonal limit for high frequency quasinormal modes and their connection to the black holes geometric characteristics. To study the photon sphere, quasinormal modes, and black hole shadow, we employ various techniques such as the Wentzel-Kramers-Brillouin method in various orders of approximation, the Poschl-Teller potential method, and Churilova’s analytical formulas. Our results indicate that the real part of the eikonal quasinormal mode frequencies of test fields are linked to the unstable circular null geodesic and are correlated with the shadow radius for a charged black hole in 4D Einstein-Gauss-Bonnet gravity. Furthermore, we found that the real part of quasinormal modes, the photon sphere and shadow radius have a lower value for charged black holes in 4D Einstein-Gauss-Bonnet gravity compared to black holes without electric charge and those of static black holes in general relativity. Additionally, we explore various analytical formulas for the photon spheres and shadows, and deduce an approximate formula for the shadow radius of charged black holes in 4D Einstein-Gauss-Bonnet gravity, based on Churilova’s method and its connection with the eikonal quasinormal modes.