INITIAL DATA FOR THE BLACK-HOLE PLUS BRILL WAVE SPACETIME

In this paper we present a new initial data set for use in numerical r elativity investigations involving black-hole-gravitational-wave inter actions. The initial data are time symmetric and are constructed on a spacelike hypersurface with the topology of a single Einstein-Rosen br idge (S-2 x R). The two ''sheets'' of the bridge are chosen to be isom etric through a two-sphere and this requires the two-sphere to be a ma rginally trapped surface. The three-metric is in the form used by Bril l and others to study time symmetric gravitational waves, the form of the wave being chosen to maintain this isometry. There are three param eters which control the amplitude, width, and range of the wave from t he isometry surface. Various physical results are determined as a func tion of these parameters including the mass of the slice, the geometry of various two-surfaces within the slice, the location and geometry o f apparent horizons, and the form of curvature and radiation quantitie s traditionally used in numerical relativity calculations. We also pre sent a linearized analysis of the data sets.