The characteristics of colliding black holes

Abstract

I review the characteristic initial value problem, its implementation as a robust computational algorithm for a 4-dimensional vacuum space-time (the PITT NULL CODE) and its application to the calculation of gravitational waveforms emitted by black holes. I describe the potential applications of the code to the binary black hole problem, via Cauchy-characteristic matching or pure characteristic evolution. In particular, the event horizon is itself a characteristic hypersurface and can be treated by characteristic methods as a stand-alone object. This allows an analytic treatment of the intrinsic geometry of the event horizon for colliding black holes which produces the pair-of-pants horizon found in the numerical simulation of the head-on-collision of black holes and the initially toroidal event horizon found in the simulation of a collapsing, rotating cluster. Most previous studies of black hole formation and merger are restricted to the axisymmetric case. However, axisymmetric horizons, like the Schwarzs...