Topological black holes in mimetic gravity

We construct some new classes of topological black hole solutions in the context of mimetic gravity. We study the uncharged and charged black holes, separately. In the absence of a potential for the mimetic field, our solutions can address the flat rotation curves of spiral galaxies and alleviate the dark matter problem without invoking any kind of particle dark matter. Thus, mimetic gravity can provide a theoretical background for understanding flat galactic rotation curves through modification of the Schwarzschild spacetime. We also investigate the casual structure and physical properties of the solutions. The presence of the mimetic field changes the asymptotic behaviour of the spacetime. We observe that in the absence of a potential, our solutions are not asymptotically flat, while, in the presence of a negative constant potential for the mimetic field, the asymptotic behaviour of the solutions can be anti de-Sitter (AdS). Finally, we explore the motion of massless and massive particles and give a list of the types of orbits. We study the differences of geodesic motion in Einstein gravity and in mimentic gravity. In contrast to Einstein gravity, massive particles always move on bound orbits and cannot escape the black hole in mimentic gravity. Furthermore, we find stable bound orbits for massless particles.