Coordinate conditions in three-dimensional numerical relativity

We put forward a few ideas on coordinate (gauge) conditions in numerical relativity. Coordinate conditions are important for long time scale simulations of relativistic systems. We demonstrate the importance of, and propose methods for, the active enforcement of coordinate properties. In particular, the constancy of the determinant of the spatial 3-metric is investigated as such a property. We propose an exceedingly simple but powerful idea for implementing elliptic coordinate conditions that not only makes possible the use of complicated elliptic conditions, but is also a number of orders of magnitude more efficient than existing methods for large-scale three-dimensional simulations.