Scattering black holes spin up and gain mass through the reabsorption of orbital angular momentum and energy radiated in gravitational waves during their encounter. In this work, we perform a series of numerical relativity simulations to investigate the spin-up and mass-gain for equal-mass black holes in a wide range of equal initial spins, ${\chi }_{\mathrm{i}}\in [-0.7,0.7]$, aligned (or antialigned) to the orbital angular momentum. We also consider a variety of initial momenta. Furthermore, we explore a range of incident angles and identify the threshold between scattering and merging configurations. The spin-up and mass-gain are typically largest in systems with incident angles close to the threshold value, large momenta, and negative (i.e., antialigned) initial spins. When evaluated at the threshold angle, we find that the spin-up decreases linearly with initial spin. Intriguingly, systems with initial spin ${\chi }_{\mathrm{i}}=0.7$ sometimes experience a spin-down, in spite of an increase in the black-hole angular momentum, due to a corresponding gain in the black-hole mass. Across the simulation suite, we find a maximum spin-up of 0.3 and a maximum increase in the black-hole mass of 15%.

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• Classical black holes
• Gravitational waves
• Numerical relativity