  When two relativistically boosted, nonspinning black holes pass by one
another on a scattering trajectory, we might expect the tidal interaction to
spin up each black hole. We present the first exploration of this effect,
appearing at fourth post-Newtonian order, with full numerical relativity
calculations. The basic setup for the calculations involves two free
parameters: the initial boost of each black hole and the initial angle between
the velocity vectors and a line connecting the centers of the black holes, with
zero angle corresponding to a head-on trajectory. To minimize gauge effects, we
measure final spins only if the black holes reach a final separation of at
least $20M$. Fixing the initial boost, we find that as the initial angle
decreases toward the scattering/nonscattering limit, the spin-up grows
nonlinearly. In addition, as initial boosts are increased from $0.42c$ to
$0.78c$, the largest observed final dimensionless spin on each black hole
increases nonlinearly from $0.02$ to $0.20$. Based on these results, we
conclude that much higher spin-ups may be possible with larger boosts, although
achieving this will require improved numerical techniques.
