New Conformally Flat Initial Data for Spinning Black Holes

We study conformally-flat initial data for an arbitrary number of spinning black holes with exact analytic solutions to the momentum constraints that combine the classical Bowen-York solution with the conformal Kerr extrinsic curvature by taking a weighted average of the Kerr and Bowen-York extrinsic curvatures, and varying the weight. We find that the curvature leading to the largest intrinsic spin, i.e. $\alpha=S/M^2_{\rm ADM}$, is neither the Kerr nor the Bowen-York extrinsic curvatures, but lies in between the two. We obtain a maximum intrinsic spin of $\alpha_{\rm max}=0.9324$. We present formulas for this new extrinsic curvature in a way that is as straightforward to code in a numerical initial data solver as the Bowen-York extrinsic curvature.