Nonsingular Yukawa-modified black holes surrounded by dark matter in 4D-Einstein-Gauss-Bonnet gravity: Shadow and QNM studies

This paper investigates the contribution of the nonsingular Yukawa-modified potential in four-dimensional Einstein-Gauss-Bonnet (EGB) gravity, focusing on a static, spherically symmetric black hole solution. These Yukawa-type corrections are described by two parameters, β and λ , that affect Newton’s law of gravity at large distances, and by a deformation parameter, ℓ 0 , which is essential at short distances. Primarily, the strongest effect is encoded in β , which alters the total mass of the black hole with additional mass proportional to β M , imitating the effects of dark matter at large distances from the black hole. In contrast, the impact due to λ is small for astrophysical values. On the other hand, EGB gravity is ruled by the Gauss-Bonnet (GB) coupling constant α , a fundamental parameter of the theory. We pay particular attention to thermodynamic stability, critical orbits, geodesics, and quasinormal modes. The results demonstrate the stability of the black hole solution for a range of values of the GB coupling constant α . Furthermore, this study investigates null geodesic motion, namely the shadow behavior, and provides intriguing results on the size of the black hole shadow.