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We use numerical simulations of scalar field dark matter evolving on a movingblack hole background to confirm the regime of validity of (semi-)analyticexpressions derived from first principles for both dynamical friction andmomentum accretion in the relativistic regime. We cover both small and largeclouds (relative to the de Broglie wavelength of the scalars), and light andheavy particle masses (relative to the BH size). In the case of a small darkmatter cloud, the effect of accretion is a non-negligible contribution to thetotal force on the black hole, even for small scalar masses. We confirm thatthis momentum accretion transitions between two regimes (wave- andparticle-like) and we identify the mass of the scalar at which the transitionbetween regimes occurs.

Relativistic drag forces on black holes from scalar dark matter clouds of all sizes