Dynamical friction from scalar dark matter in the relativistic regime

Light bosonic scalars (e.g. axions) may form clouds around black holes via superradiant instabilities, or via accretion if they form some component of the dark matter. It has been suggested that their presence may lead to a distinctive dephasing of the gravitational wave signal when a small compact object spirals into a larger black hole. Motivated by this, we study numerically the dynamical friction force on a black hole moving at relativistic velocities in a background scalar field with an asymptotically homogeneous energy density. We show that the relativistic scaling is analogous to that found for supersonic collisional fluids, assuming an approximate expression for the pressure correction which depends on the velocity and scalar mass. While we focus on a complex scalar field, our results confirm the expectation that real scalars would exert a force which oscillates between positive and negative values in time with a frequency set by the scalar mass. The complex field describes the time averaged value of this force, but in a real scalar the rapid force oscillations could in principle leave an imprint on the trajectory. The approximation we obtain can be used to inform estimates of dephasing in the final stages of an extreme mass ratio inspiral.