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

Abstract

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 $\ell_0$, 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 $β\mathcal{M}$, 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.