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.

6.1 The constraints in the harmonic gauge

6.2 The constraints in the new systems: Theoretical considerations

6.3 The constraints in the new systems: Numerical considerations

6.4 The constraints in the initial-boundary value problem

6.2 The constraints in the new systems: Theoretical considerations

6.3 The constraints in the new systems: Numerical considerations

6.4 The constraints in the initial-boundary value problem

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