|Abstract:||We present results from numerical evolutions of vacuum black hole spacetimes in 3D Cartesian coordinates. We first studied the Schwarzschild spacetime, comparing
extensively with lD studies. We show that although accurate 3D evolutions are
possible, there are a number of difficulties in evolving 3D black holes, for which we
suggest approaches to overcome. With current limits on computer memory sizes, we show that with certain slicing conditions, the black hole can be evolved to about
t = 50M, where M is the black hole mass. We also present the first 3D evolutions
of colliding black holes, with evolutions of the axisymmetric Misner two-black hole
initial data sets. Here we demonstrate that the techniques we developed for the
Schwarzschild case carry over to other spacetimes. We also demonstrate the feasibility of extracting gravitational wave signals during 3D evolutions. We present new, fully 3D distorted black hole initial data sets, extending Bernstein's axisymmetric data sets in a straightforward way. Metric functions and waveforms from evolutions of these data sets in the axisymmetric limit are shown to agree with 2D calculations. For evolutions of the non-axisymmetric sets, which are the first truly 3D black hole data sets to be evolved, all non-trivial wave modes through l = 4 are presented. Finally, we point the way towards studying the evolution of these data sets with perturbation theory.