Topological black holes in mimetic gravity

In this paper, we construct some new classes of topological black hole solutions in the context of mimetic gravity and investigate their properties. We study the uncharged and charged black holes, separately. We find the following novel results: (i) In the absence of a potential for the mimetic field, black hole solutions can address the flat rotation curves of spiral galaxies and alleviate the dark matter problem without invoking particle dark matter. Thus, mimetic gravity can provide a theoretical background for understanding flat galactic rotation curves through modifying Schwarzschild space-time. (ii) We also investigate the casual structure and physical properties of the solutions. 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 solutions are asymptotically anti-de Sitter (AdS). (iii) 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 the Einstein gravity and in mimetic gravity. In contrast to the Einstein gravity, massive particles always move on bound orbits and cannot escape the black hole in mimetic gravity. Furthermore, we find stable bound orbits for massless particles.