How to avoid artificial boundaries in the numerical calculation of black hole spacetimes

This is the first of a series of papers describing a numerical implementati on of the conformally rescaled Einstein equation, an implementation designe d to calculate asymptotically flat spacetimes, especially spacetimes contai ning black holes. We derive the new first-order time evolution equations to be used in the sc heme. These time evolution equations can either be written in symmetric hyp erbolic or in flux-conservative form. Since the conformally rescaled Einste in equation, also called the conformal field equations, formally allow us t o place the grid boundaries outside the physical spacetime, we can modify t he equations near the grid boundaries and obtain a consistent and stable di scretization. Even if we calculate spacetimes containing black holes, there is no need to introduce artificial boundaries in the physical spacetime, w hich then would complicate, influence or even exclude the computation of ce rtain spacetime regions.