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

Abstract: 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.