In this paper, we consider black holes in the consistent Aoki-Gorji-Mukohyama theory of the four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity in the presence of Born-Infeld (BI) nonlinear electrodynamics. We study several optical features of these black holes such as the shadow radius, energy emission rate and deflection angle, and analyse the effect of the coupling constants, the electric charge and cosmological constant on the considered optical quantities. Furthermore, we also employ the connection between the shadow radius and quasinormal modes (QNMs) and investigate small scalar perturbations around the black hole solution. We show that the variation of the parameters of the theory provide specific signatures on the optical features of the BI charged black hole solution, thus leading to the possibility of directly testing this consistent Aoki-Gorji-Mukohyama 4D EGB black hole model by using astrophysical observations.

In this work, we consider a recent novel regular black hole solution, which we denote the Simpson-Visser black-bounce model and investigate circular null geodesics to find the connection between the photon sphere, the event horizon and the black hole shadow radii. We also study the energy emission rate for this geometry and discuss how the parameters of the model affect the emission of particles around the black hole. Furthermore, we compare the resulting shadow of this regular black hole with observational data of the Event Horizon Telescope and find the allowed regions of the model parameters for which the obtained shadow is consistent with the data. Finally, we employ the correspondence between the quasinormal modes in the eikonal limit and shadow radius to study the scalar field perturbations in this background.

An alternative theory of gravity that has attracted much attention recently is the novel four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity. The theory is rescaled by the Gauss-Bonnet (GB) coupling constant α→α/(D−4) in D dimensions and redefined as four-dimensional gravity in the limit D→4. Thus, in this manner, the GB term yields a non-trivial contribution to the gravitational dynamics. In fact, regularized black hole solutions and applications in the novel 4D EGB gravity have also been extensively explored. In this work, motivated by recent astrophysical observations, we present an in-depth study of the optical features of AdS black holes in the novel 4D EGB gravity coupled to exponential nonlinear electrodynamics (NED), such as the shadow geometrical shape, the energy emission rate, the deflection angle and quasinormal modes. Taking into account these dynamic quantities, we investigate the effects on the black hole solution by varying the parameters of the models. More specifically, we show that the variation of the GB and NED parameters, and of the cosmological constant, imprints specific signatures on the optical features of AdS black holes in the novel 4D EGB gravity coupled to nonlinear electrodynamics, thus leading to the possibility of directly testing these black hole models by using astrophysical observations.

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