  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.
