INITIAL DATA FOR THE BLACK-HOLE PLUS BRILL WAVE SPACETIME

In this paper we present a new initial data set for use in numerical relativity investigations involving black-hole-gravitational-wave interactions. The initial data are time symmetric and are constructed on a spacelike hypersurface with the topology of a single Einstein-Rosen bridge (S-2 x R). The two ''sheets'' of the bridge are chosen to be isometric through a two-sphere and this requires the two-sphere to be a marginally trapped surface. The three-metric is in the form used by Brill and others to study time symmetric gravitational waves, the form of the wave being chosen to maintain this isometry. There are three parameters which control the amplitude, width, and range of the wave from the isometry surface. Various physical results are determined as a function of these parameters including the mass of the slice, the geometry of various two-surfaces within the slice, the location and geometry of apparent horizons, and the form of curvature and radiation quantities traditionally used in numerical relativity calculations. We also present a linearized analysis of the data sets.