We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the solution of a Cauchy evolution of the nonlinear Einstein field equations to a set of one-dimensional linear equations obtained through perturbation techniques over a curved background. We discuss the validity of this approach in the case of linear and mildly nonlinear gravitational waves and show how a numerical module developed for this purpose is able to provide an accurate and numerically convergent description of the gravitational wave propagation and a stable numerical evolution.

We present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einstein's equations to a set of one-dimensional linear wave equations on a curved background. We illustrate the mathematical properties of our approach and discuss a numerical module we have constructed for this purpose. This module implements the perturbative matching approach in connection with a generic three-dimensional numerical relativity simulation. Tests of its accuracy and second-order convergence are presented with analytic linear wave data.

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...

We report new results which establish that the accurate three-dimensional numerical simulation of generic single-black-hole spacetimes has been achieved by characteristic evolution with unlimited long term stability. Our results include distorted, moving, and spinning single black holes, with evolution times up to 60 000M. [S0031-9007(98)