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

In this paper, we study with numerical relativity the spin induction effect within close hyperbolic encounters for equal-mass black holes. We review the initially nonspinning 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 close hyperbolic encounter. 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 spins with respect to the initial spins are well-fitted by a parabola. When considering 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 new phenomena suggest that dense black hole clusters are very interesting dynamical systems where black hole spins may acquire a non trivial distribution, both for aligned and isotropic spins.
Comment: 12 pages, 10 figures, 3 tables