6 The Role of the Constraints

In this section, I analyze the role the constraint equations play in these new formulations. I will start by analyzing how the equations were handled in the original proof of well posedness. Then, I discuss what has been said recently and what has to be done in the future, both for theoretical considerations and for numerical work. In particular, I discuss the role of the constraints in the initial-boundary value problem, a problem which has still to be fully solved, but which nevertheless is applied in most of the numerical simulations.