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.

在本文中，我们考虑了在 Born-Infeld (BI) 非线性电动力学存在的情况下，四维 Einstein-Gauss-Bonnet (4D EGB) 引力的一致 Aoki-Gorji-Mukohyama 理论中的黑洞。我们研究了这些黑洞的几个光学特征，如阴影半径、能量发射率和偏转角，并分析了耦合常数、电荷和宇宙学常数对所考虑的光学量的影响。此外，我们还利用了阴影半径和准正规模式 (QNM) 之间的联系，并研究了黑洞解周围的小标量扰动。我们表明，理论参数的变化为 BI 带电黑洞解决方案的光学特征提供了特定的特征，