Dynamic vacuum spacetimes in a computer

Abstrakt: Despite the tremendous success of mathematical general relativity which revealed among others surprising features of the geometry of rotating (Kerr) black holes and developed approximation techniques to study early stages of their inspiral, the necessity to describe completely the merger of two black holes lead to a substantial progress of numerical relativity. This field necessarily uses techniques of modern computer science to amass and command number crunching capabilities of current computers as well as numerical methods for partial differential equations, but the successful computer simulations also required new type of answers to questions "what is the black hole" and "what kind of equations are the Einstein ones". From this perspective I will also mention some results on hyperbolicity analysis of 3+1 reductions of Einstein equations and coordinate choice and horizon formation for collapse of gravitational waves into a black hole.