Notice that even when
, the evolution system (4.27, 4.28, 4.20, 4.21) is not equivalent to the harmonic system
discussed in Section 4.1. In the former case, the harmonic constraint is exactly enforced in order to obtain evolution equations
for the lapse and shift; while in the latter case first derivatives of the harmonic constraint are combined with the Hamiltonian
and momentum constraints; see Eq. (4.13).