Induced Spins from Scattering Experiments of Initially Nonspinning Black Holes

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.