We consider the initial data problem for several black holes in vacuum with arbitrary momenta and spins on a three space with punctures. We compactify the internal asymptotically flat regions to obtain a computational domain without inner boundaries. When treated numerically, this leads to a significant simplification over the conventional approach which is based on throats and isometry conditions. In this new setting it is possible to obtain existence and uniqueness of solutions to the Hamiltonian constraint.

In this paper we study a new family of black hole initial data sets corresponding to distorted "Kerr" black holes with moderate rotation parameters, and distorted Schwarzschild black holes with even- and odd-parity radiation. These data sets build on the earlier rotating black holes of Bowen and York and the distorted Brill wave plus black hole data sets. We describe the construction of this large family of rotating black holes. We present a systematic study of important properties of these data sets, such as the size and shape of their apparent horizons, and the maximum amount of radiation that can leave the system during evolution. These data sets should be a very useful starting point for studying the evolution of highly dynamical black holes and can easily be extended to 3D.

We present the first simulations of non-head-on (grazing) collisions of binary black holes in which the singularities are excised from the simulation. Initially equal mass $m$ black holes (spinning or not) are separated by $\approx 10m$ and with impact parameter $\approx 2m$. Evolutions to $t\approx 35m$ are obtained where two separate horizons are present for $t\approx 3.8m$; then a single enveloping horizon forms indicating that the holes merged. Apparent horizon area estimates suggest gravitational radiation of about $2\%–3\%$ of the total mass. The evolutions end after a moderate amount of time because of instabilities.