Robust evolution system for numerical relativity

The paper combines theoretical and applied ideas which have been previously considered separately into a single set of evolution equations for numerical relativity. New numerical ingredients are presented which avoid gauge pathologies and allow one to perform robust three-dimensional calculations. The potential of the resulting numerical code is demonstrated by using black hole space-times as a test bed. The evolution of a Schwarzschild black hole can be followed up to times greater than one hundred black hole masses. A distorted black hole is also modeled from the Misner double black hole initial data, the two holes being surrounded by a single horizon.