We examine the interactions of a black hole with a massless scalar field using a coordinate system which extends ingoing Eddington-Finkelstein coordinates to dynamic spherically symmetric-spacetimes. We avoid problems with the singularity by excising the region of the black hole interior to the apparent horizon. We use a second-order finite difference scheme to solve the equations. The resulting program is stable and convergent and will run forever without problems. We are able to observe quasi-normal ringing and power-law tails as well an interesting nonlinear feature.

We extend the investigation of the gravitational collapse of a spherically symmetric Yang-Mills field in Einstein gravity and show that, within the black hole regime, a new kind of critical behavior arises which separates black holes formed via type I collapse from black holes formed through type II collapse. Further, we provide evidence that these new attracting critical solutions are in fact the previously discovered colored black holes with a single unstable mode. ͓S0556-2821͑99͒03024-6͔

We model a radiating, moving black hole in terms of a worldtube-nullcone boundary value problem. We evolve this data in the region interior to the worldtube but exterior to a trapped surface by means of a characteristic evolution based upon a family of ingoing null hypersurfaces. Data on the worldtube is induced from a Schwarzschild spacetime but the worldtube is allowed to move relative to the static Schwarzschild trajectories. When the worldtube is stationary (static or rotating in place), a distorted black hole inside it evolves to equilibrium with the Schwarzschild boundary. A boost of the worldtube with respect to the Schwarzschild black hole does not affect these results. The code also stably tracks an unlimited number of orbits when the worldtube wobbles periodically. The work establishes that characteristic evolution can evolve a spacetime with a distorted black hole moving on a 3-dimensional grid with the controlled accuracy and long term stability necessary to investigate new facets of black hole physics.

We present a new method for treating the inner Cauchy boundary of a black hole spacetime by matching to a characteristic evolution. We discuss the advantages and disadvantages of such a scheme relative to Cauchy-only approaches. A prototype code, for the spherically symmetric collapse of a self-gravitating scalar field, shows that matching performs at least as well as other approaches to handling the inner boundary.

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