Extra-large remnant recoil velocities and spins from near-extremal-Bowen-York-spin black-hole binaries

We evolve equal-mass, equal-spin black-hole binaries with specific spins of a/m(H)similar to 0.925, the highest spins simulated thus far and nearly the largest possible for Bowen-York black holes, in a set of configurations with the spins counteraligned and pointing in the orbital plane, which maximizes the recoil velocities of the merger remnant, as well as a configuration where the two spins point in the same direction as the orbital angular momentum, which maximizes the orbital hangup effect and remnant spin. The coordinate radii of the individual apparent horizons in these cases are very small and the simulations require very high central resolutions (h similar to M/320). We find that these highly spinning holes reach a maximum recoil velocity of similar to 3300 km s(-1) (the largest simulated so far) and, for the hangup configuration, a remnant spin of a/m(H)similar to 0.922. These results are consistent with our previous predictions for the maximum recoil velocity of similar to 4000 km s(-1) and remnant spin; the latter reinforcing the prediction that cosmic censorship is not violated by merging highly spinning black-hole binaries. We also numerically solve the initial data for, and evolve, a single maximal-Bowen-York-spin black hole, and confirm that the 3-metric has an O(r(-2)) singularity at the puncture, rather than the usual O(r(-4)) singularity seen for nonmaximal spins.