We present here an alternative approach to data setting for spacetimes with multiple moving black holes generalizing the Kerr-Schild form for rotating or non-rotating single black holes to multiple moving holes. Because this scheme preserves the Kerr-Schild form near the holes, it selects out the behaviour of null rays near the holes, may simplify horizon tracking, and may prove useful in computational applications. For computational evolution, a discussion of coordinates (lapse function and shift vector) is given which preserves some of the properties of the single-hole Kerr-Schild form.

We present the first simulations of non-headon (grazing) collisions of binary black holes in which the black hole singularities have been excised from the computational domain. Initially two equal mass black holes m are separated a distance ≈ 10m and with impact parameter ≈ 2m. Initial data are based on superposed, boosted (velocity ≈ 0.5c) solutions of single black holes in Kerr-Schild coordinates. Both rotating and non-rotating black holes are considered. The excised regions containing the singularities are specified by following the dynamics of apparent horizons. Evolutions of up to t ≈ 35m are obtained in which two initially separate apparent horizons are present for t ≈ 3.8m. At that time a single enveloping apparent horizon forms, indicating that the holes have merged. Apparent horizon area estimates suggest gravitational radiation of about 2.6% of the total mass. The evolutions end after a moderate amount of time because of instabilities.Introduction: Gravitational wave detectors [1] will soon begin searching for gravitational radiation from astrophysical binary compact objects. To understand these observations, and to predict parameter regimes in which to search for their radiation, efforts are underway to model the interaction of compact sources. We report here a direct numerical simulation of interacting spinning black hole binaries, in genuinely hyperbolic (nonheadon) trajectories. The initial spin angular momenta evolved here are either zero, or parallel to each other and perpendicular to the orbital plane. The interior of the equal mass holes and their interior singularities are excised from the computation. (Our method is neither restricted to equal masses nor to parallel spins). Evolution is carried out in a Cauchy scheme, in which the state of the gravitational system (the 3-spatial metric g ab ) and its rate of change (the 3-spatial extrinsic curvature K ab ) are specified at one instant (i.e. on a 3-dimensional spacelike hypersurface) and are then stepped to the next instant using an "ADM" [2] form of the Einstein evolution equations [3]. The evolution is unconstrained, and maintenance of the constraint functions with small error is verified throughout the run.This work extends previous work on headon encounters [4][5][6][7]. It is comparable to recent results of Brügmann [8]: non-headon black hole evolution through to significant interaction and merger. But our approach has a novel feature: the singularity-excising character of the computation of generic encounters which allows "natural" motion of the black holes through the computational

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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 ∼ 6M at 0.1c during a total evolution of duration ∼ 60M . The accurate computational modeling of black-hole interactions is essential to the confident detection of astrophysical gravitational radiation by future space-based detectors such as LISA and by the LIGO/VIRGO/GEO complex of ground-based detectors currently under construction. The sensitivity of these detectors will be significantly enhanced if accurate computer simulations of black-hole mergers can produce predictions of radiation waveforms [1]. The Binary Black Hole Grand Challenge Alliance [2] was funded in September 1993 to develop the computational infrastructure necessary accurately to simulate the coalescence of black-hole binaries. The primary objective of the resulting code will be the production of waveforms from binary black hole mergers. In this Letter we report on an important step towards achieving such simulations.A key difficulty in evolving black-hole spacetimes is handling the curvature singularity contained within each hole. The only viable means of accomplishing this over time scales required for binary coalescence appears to be black-hole excision: exclude all or part of the black-hole interior (and the singularity) from the computational domain and evolve only the exterior region [3,4

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. [S0031-9007(98)05380-0] PACS numbers: 04.25. Dm, 04.30.Db, 04.70.Bw Numerical relativity represents the only currently viable method for obtaining solutions to Einstein equations for highly dynamical and strong field sources of gravitational radiation. Using these techniques to study coalescing black hole binaries is the purpose of the multi-institutional Binary Black Hole "Grand Challenge" Alliance effort [1] which is presently underway in the United States. This effort is also motivated by the prospect of observations with the next generation of gravitational wave detectors.In addition to tremendous demands on computational resources, implementing the standard 3 1 1 [2,3] formulation of Einstein theory as a Cauchy problem [4] is complicated considerably by the necessity of imposing boundary conditions which maintain numerical accuracy and the physical correctness of the solution. Both inner and outer boundary conditions have received considerable attention. Recent efforts on interior boundaries have focused on the excision of the interior of the black hole from the computational domain (see, for example, [5]). This paper will concentrate on the problem of outer boundary conditions applied at a finite radius around a source of gravitational waves.Proper boundary conditions on spacelike slices of asymptotically flat spacetimes are essential for the accurate computation of the gravitational wave forms produced in the strong field region that represent the observationally relevant aspect of the computation. Since it is not feasible to simulate on spacelike slices out to arbitrarily large distances from the source, it is necessary to extract gravitational waves comparatively near the strong field region and to have boundary conditions that allow radiation to pass cleanly off the mesh. If poor outgoing boundary conditions are imposed, spurious radiation is produced which can contaminate the computed gravitational wave form. Additionally, the outer boundary is usually close enough to the isolated source that backscatter of radiation from curvature is significant. This source of incoming radiation needs to be built into the outer boundary conditions. An approach to the extraction of gravitational wave information and the computation of outer boundary conditions that exploits the matching of the interior numerical solution with an exterior perturbative solution on spacelike slices has been developed during the past decade and applied to a number of different physical scenarios [6][7][8]. Extension of these techniques to three-dimensional (3D) simulations has been one of the ef...