Constraint-preserving boundary conditions in the Z4 numerical relativity formalism

The constraint-preserving approach is discussed in parallel with other recent developments with the goal of providing consistent boundary conditions for numerical relativity simulations. The case of the first-order version of the Z4 system is considered, and constraint-preserving boundary conditions of the Sommerfeld type are provided. The stability of the proposed boundary conditions is related to the choice of the ordering parameter. This relationship is explored numerically and some values of the ordering parameter are shown to provide stable boundary conditions in the absence of corners and edges. Maximally dissipative boundary conditions are also implemented. In this case, a wider range of values of the ordering parameter is allowed, which is shown numerically to provide stable boundary conditions even in the presence of corners and edges.