Spin induction from scattering of two spinning black holes in dense clusters

In this paper, we use numerical relativity to study the spin induction effect within close hyperbolic encounters of initially spinning black holes. We review the initially non-spinning case and explore the cases of initially aligned, anti-aligned and orthogonal spins with respect to the orbital angular momentum $\vec L$. We find that, for a given initial effective spin, the black hole with a smaller initial spin acquires a greater spin-up than the other black hole after the interaction. We study three different scenarios regarding initial effective spin ($\chi_{\rm eff}=-0.1, \ 0.0, \ 0.1$), using three different scattering angles in order to obtain maximally spin-inducing scenarios. We also find that the final effective spin-ups with respect to the initial spins are well-fitted by a parabola. For spins orthogonal to $\vec L$, we observe that the black hole spins precess, and that the induced spin in the $z$-direction depends quadratically on the value of the initial spins. These phenomena suggest that dense black hole clusters present a rich spin dynamics, where black hole spins may acquire non-trivial distributions.