### 6.1 The constraints in the harmonic gauge

In the harmonic gauge, the role of the constraint equations as such is hidden. This is because the
constraint equations become evolution equations due to the gauge choice. Indeed, in the full harmonic gauge
all components of the Einstein tensor become a big second order hyperbolic equation for the metric
components. The need for the constraints to be satisfied at the initial surface enters the picture because it
implies that the first time derivative of the gauge condition must vanish there in order to guarantee that the
constraints vanish everywhere. Thus the question about the preservation of the constraint equations
does not appear here. At most one can say it has been traded for the question of the gauge
consistency.