(ed.). Gravitational waves (IOP, 2001)(422s).

382 Numerical relativity1D code [45]. The errors were found to be greatly reduced when compared even tothe 1D evolution with singularity avoiding slicings. Another 3D implementationof the basic technique was provided by Brügmann [60].This was a proof of principle, but more general treatments are following.Daues extended this work to a full range of shift conditions [6], including the full3D minimal distortion shift [10]. He also applied these techniques to dynamicBHs, and collapse of a star to form a BH, at which point the horizon is detected,the region interior to the horizon excised, and the evolution continued withAHBC. The focus of this work has been on developing general gauge conditionsfor single BHs without movement through a grid. Under these conditions, BHshave been accurately evolved well beyond t = 100M. The NSF Black HoleGrand Challenge Alliance has been focused on the development of 3D AHBCtechniques for moving Schwarzschild BHs [7]. In this work, analytic gaugeconditions are provided, which are chosen to make the evolution static, althoughthe numerical evolution is allowed to proceed freely. This moving hole is thefirst successful 3D test of populating grid points with data as they emerge in theBH wake. The recent, as yet unpublished, work of Huq et al has successfullyevolved full 3D grazing collisions through about t = 10M ADM , including thetopology change from two excision regions to a single one, while Alcubierre et alhave recently evolved Schwarzschild black holes in 3D, with rather general gaugeconditions, for well over t = 4000M ADM with less than a few per cent error!These new results are significant achievements, and show that the basictechniques outlined above are not only sound, but are also practically realizablein a 3D numerical code. However, there is still a significant amount of work to bedone! The techniques have yet to be applied carefully to distorted BHs, with testsof the waveforms emitted. There are still clearly many steps to be taken beforethe techniques will be successfully applied to the general BH merger problem.18.4 Tools for analysing the numerical spacetimesWe now turn to the description of several important tools that have been developedto analyse the results of a numerical evolution, carried out by some numericalevolution scheme. The evolution will generally provide metric functions ona grid, but as described above these functions are highly dependent on boththe coordinate system and gauge in which the system is evolved. Determiningphysical information, such as whether a black hole exists in the data, or whatgravitational waveforms have been emitted, are the subjects of this section.18.4.1 Horizon findersAs described earlier, black holes are defined by the existence of an event horizon(EH), the surface of no return from which nothing, not even light, can escape.The event horizon is the boundary that separates those null geodesics that reachinfinity from those that do not. The global character of such a definition implies