The characteristic treatment of black holes

Abstract

The characteristic initial value problem has been successfully implemented as a robust computational algorithm (the PITT NULL CODE) to evolve 4-dimensional vacuum space-times. It has been applied to the calculation of gravitational waveforms emitted by black holes and to the event horizon structure in the merger of black holes. The characteristic code also has potential application to the binary black hole problem via Cauchy-characteristic matching. Because the event horizon is itself a characteristic hypersurface, it can be analyzed by characteristic techniques as a stand-alone object. We have developed an analytic conformal model of null hypersurfaces which gives new insight into the intrinsic geometry of the pair-of-pants horizon found in the numerical simulation of the head-on collision of black holes and into the initially toroidal horizon found in the simulation of a collapsing, rotating cluster. Most studies of black hole formation and merger have been restricted to axisymmetry. However, axisymmetric horizons, like the Schwarzschild horizon, are non-generic. When applied to a non-axisymmetric horizon, the characteristic approach reveals substantially new features. In particular, coalescing black holes generically go through a toroidal phase before they become spherical. The conformal structure of the event horizon supplies part of the data for a simulation of the exterior space-time. This provides a new way to calculate the post-merger waveforms from a binary black hole inspiral.