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

380 Numerical relativityFigure 18.1. A spacetime diagram showing the formation of a BH, and time slicestraditionally used to foliate the spacetime in traditional numerical relativity with singularityavoiding time slices. As the evolution proceeds, pathologically warped hypersurfacesdevelop, leading to unresolvable gradients that cause numerical codes to crash.This has the consequence that there will be a region inside the horizon that simplyhas no numerical data. To an outside observer no information will be lost sincethe regions cut away are unobservable. Because the time slices will not needsuch sharp bends to the past, this procedure will drastically reduce the dynamicrange, making it easier to maintain accuracy and stability. Since the singularityis removed from the numerical spacetime, there is in principle no physical reasonwhy BH codes cannot be made to run indefinitely without crashing.We spoke innocently about the BH horizon, but did not distinguish betweenthe apparent and event horizon. These are very different concepts! Whilethe event horizon, which is roughly a null surface that never reaches infinityand never hits the singularity, may hide singularities from the outside world inmany situations, there is no guarantee that the apparent horizon, which is the(outermost) surface that has instantaneously zero expansion everywhere, evenexists on a given slice! (By ‘zero expansion’ we mean that the surface area ofoutgoing bundles of photons normal to the surface is constant. Hence, the surfaceis ‘trapped’.) Methods for finding event horizons in numerical spacetimes are nowknown, and will be discussed below. However, event horizons can only be foundafter examining the history of an evolution that has been already been carried