Dark matter effects of a black hole with nonsingular Yukawa-modified potential in Einstein-Gauss-Bonnet Gravity

This paper investigates the contribution of the nonsingular Yukawa-modified potential in the context of four-dimensional Einstein-Gauss-Bonnet (EGB) gravity modeling by a static and spherically symmetric black hole solution. These Yukawa-type corrections are essentially described along two parameters, β and λ, affecting Newton's law of gravity at large distances, and 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 βℳ, imitating the effects of dark matter at large distances from the black hole. In contrast, the effect due to λ is small for astrophysical values. On the other hand, the 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 stability of the black hole solution for a range of values of the GB coupling constant α. Furthermore, this study investigates the null geodesic motion, namely the shadow behavior, providing intriguing results in relation to the size of the black hole shadow.