We present a series of test-beds for numerical codes designed to find apparent horizons. We compare three apparent horizon finders that use different numerical methods: one of them in axisymmetry and two which are fully three dimensional. We concentrate first on a toy model that has a simple horizon structure, and then go on to study single and multiple black hole datasets. We use our finders to look for apparent horizons in Brill wave initial data where we discover that some results published previously are not correct. For pure wave and multiple black hole spacetimes, we apply our finders to survey parameter space.

We present techniques and methods for analyzing the dynamics of event horizons in numerically constructed spacetimes. There are three classes of analytical tools we have investigated. The first class consists of proper geometrical measures of the horizon which allow us comparison with perturbation theory and powerful global theorems. The second class involves the location and study of horizon generators. The third class includes the induced horizon 2-metric in the generator comoving coordinates and a set of membrane-paradigm like quantities. Applications to several distorted, rotating, and colliding black hole spacetimes are provided as examples of these techniques.

Binary black-hole interactions provide potentially the strongest source of gravitational radiation for detectors currently under development. We present some results from the Binary Black Hole Grand Challenge Alliance three-dimensional Cauchy evolution module. These constitute essential steps towards modeling such interactions and predicting gravitational radiation waveforms. We report on single black-hole evolutions and the first successful demonstration of a black hole moving freely through a three-dimensional computational grid via a Cauchy evolution: a hole moving near 6M at 0.1c during a total evolution of duration near 60M.

We describe a grid generation procedure designed to construct new classes of orthogonal coordinate systems for binary black hole spacetimes. The computed coordinates offer an alternative approach to current methods, in addition to providing a framework for potentially more stable and accurate evolutions of colliding black holes. As a particular example, we apply our procedure to generate appropriate numerical grids to evolve Misner's axisymmetric initial data set representing two equal mass black holes colliding head-on. These new results are compared with previously published calculations, and we find generally good agreement in both the waveform profiles and total radiated energies over the allowable range of separation parameters. Furthermore, because no specialized treatment of the coordinate singularities is required, these new grids are more easily extendible to unequal mass and spinning black hole collisions.

We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three dimensional numerical relativity code.

We report new results which establish that the accurate 3-dimensional numerical simulation of generic single-black-hole spacetimes has been achieved by characteristic evolution with unlimited long term stability. Our results cover a selection of distorted, moving and spinning single black holes, with evolution times up to 60,000M.

G. B. Cook, M. F. Huq, S. A. Klasky, M. A. Scheel, A. M. Abrahams, A. Anderson , P. Anninos, T. W. Baumgarte, N. T. Bishop, S. R. Brandt, J. C. Browne, K. Camarda, M. W. Choptuik, C. R. Evans , L. S. Finn, G. C. Fox, R. Gómez, T. Haupt, L. E. Kidder, P. Laguna, W. Landry, L. Lehner, J. Lenaghan , R. L. Marsa, J. Masso, R. A. Matzner, S. Mitra, P. Papadopoulos, M. Parashar, L. Rezzolla, M. E. Rupright , F. Saied, P. E. Saylor, E. Seidel, S. L. Shapiro, D. Shoemaker, L. Smarr, W. M. Suen , B. Szilágyi, S. A. Teukolsky, M. H. P. M. van Putten, P. Walker, J. Winicour, J. W. York Jr . Cornell University, Ithaca, New York 14853 The University of Texas at Austin, Austin, Texas 78712 Syracuse University, Syracuse, New York 13244-4100 University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 J. P. Morgan, 60 Wall St., New York, New York 10260 University of North Carolina, Chapel Hill, North Carolina 27599 University of South Africa, P.O. Box 392, Pretoria 0001, South Africa Penn State University, University Park, Pennsylvania 16802 Northwestern University, Evanston, Illinois 60208 University of Pittsburgh, Pittsburgh, Pennsylvania 15260 Washington University, St. Louis, Missouri 63130