A numerical framework for studying asymptotic quantities

In this contribution we present an overview of our work on the numerical simulation of the perturbation of a black hole space-time by incoming gravitational waves. The formulation we use is based on Friedrich's general conformal equations which have the unique property that they allow access to the asymptotic region of an asymptotically regular space-time. In our approach we set up an initial boundary value problem on a finite boundary, which cleanly separates the initial conditions, a static black hole, from the perturbation, an incoming gravitational wave specified by a spin-2 function on the time-like boundary. The main advantage of this approach is that the finite boundary expands fast enough to reach null-infinity where the asymptotic properties can be studied. This provides, for the first time, a direct relationship between finite initial and boundary data and asymptotic quantities within one simulation. We discuss the possibilities and limitations of this approach.