Shadow of extreme compact charged objects in consistent 4-dimensional Einstein–Gauss–Bonnet gravity

In order to better describe gravitational phenomena on both very small and cosmological scales, there have been constant attempts to generalize and expand the theory of General Relativity (GR) since its inception. The Einstein–Gauss–Bonnet (EGB) theory is one such extension that adds spacetime corrections related to curvature. Since the standard Gauss–Bonnet term is purely topological, it does not contribute to the field equations in four dimensions. To get around this restriction, however, an invariant four-dimensional limit [Formula: see text] has been developed. In this work, we study Extreme Compact Charged Objects (ECCOs), which can resemble black holes, in a gravity framework that is compatible with Einstein–Gauss–Bonnet in four dimensions. Our main goal is to compare theoretical predictions with Event Horizon Telescope (EHT) observational data in order to constrain the Gauss–Bonnet coupling constant [Formula: see text]. In order to achieve this, we investigate important optical characteristics like the shadow, light-bending angle, and other associated observables, as well as the geodesic structure of ECCO spacetimes in EGB gravity. Finally, we apply these findings to constrain the Gauss–Bonnet constant.