Spin Dependence in Computational Black-Hole Data

We have implemented an parallel multigrid solver, to solve the initial data problem for $3+1$ General Relativity. This involves solution of elliptic equations derived from the Hamiltonian and the momentum constraints. We use the conformal transverse-traceless method of York and collaborators, which consists of a conformal decomposition with a scalar $\phi$ that adjusts the metric, and a vector potential $w^i$ that adjusts the longitudinal components of the extrinsic curvature. The constraint equations are then solved for these quantities $\phi$, $w^i$ such that the complete solution fully satisfies the constraints. We apply this technique to confirm theoretical expectations for the spin -orientation and -separation dependence in the case of spinning interacting black holes, and we investigate some of the nonlinear effects in initial data for binary black hole interactions.