Constraint-preserving Sommerfeld conditions for the harmonic Einstein   equations
  The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A new formulation of constraint-preserving boundary conditions of the Sommerfeld type for such systems has recently been proposed. We implement these boundary conditions in a nonlinear 3D evolution code and test their accuracy. 
M. C. Babiuc, H-O. Kreiss, Jeffrey Winicour