Gravitational Magnus effect from scalar dark matter

In fluid dynamics, the Magnus effect is the force perpendicular to the motion of a spinning object as it moves through a medium. In general relativity, an analogous effect exists for a spinning compact object moving through matter, purely as a result of gravitational interactions. In this work we consider a Kerr black hole moving at relativistic velocities through scalar dark matter that is at rest. We simulate the system numerically and extract the total spin-curvature force on the black hole perpendicular to its motion. We confirm that the force scales linearly with the dimensionless spin parameter $a/M$ of the black hole up to $a/M = 0.99$, and measure its dependence on the speed $v$ of the black hole in the range $0.1 \le v \le 0.55$ for a fixed spin. Compared to previous analytic work applicable at small $v$, higher-order corrections in the velocity are found to be important: the total force is nonzero, and the dependence is not linear in $v$. We find that in all cases the total force is in the opposite direction to the hydrodynamical analogue, although at low speeds it appears to approach the expectation that the Weyl and Magnus components cancel. Spin-curvature effects may leave an imprint on gravitational wave signals from extreme mass-ratio inspirals, where the secondary black hole has a nonnegligible spin and moves in the presence of a dark matter cloud. We hope that our simulations can be used to support and extend the limits of analytic results, which are necessary to better quantify such effects in the relativistic regime.