Astrophysical black holes do not exist in vacuum, and their motion is affected by the galactic environment. As a black hole moves it attracts stars and matter, creating a wake that, in turn, exerts an effective friction slowing down the black hole. This force is known as dynamical friction, and has significant consequences, ranging from the formation of supermassive black hole binaries to modifications in the phase of binary mergers. In this work we explore the motion of spinning black holes on a medium. We find that the classical drag along the velocity direction is modified and two novel forces appear: a rotational force, which in the context of fluid dynamics is dubbed the Magnus force, and a lift, orthogonal to the direction of motion. We develop a first-principles fully-relativistic treatment of these spin-induced aerodynamic forces in two types of environment: i) collisionless corpuscular matter and ii) a light scalar field, exploring the differences between both cases. In both cases we find that the total rotational force acts precisely in the opposite direction as compared to the classical set-up of a spinning ball moving through a fluid. Finally, we comment on the consequences of these new effects for astrophysics and gravitational wave observations.

15 pages, 8 figures, minor update to text and references