Momentum constraint
= Momentum constraint
{title2=$\mathcal H_i=-2D_j(\pi^j{}_i/\sqrt h)=0$}
The momentum constraint is the equation obtained by varying the <shift vector> in the <Hamiltonian formulation of general relativity>. It expresses the tangential-normal projection of the <Einstein field equations> and generates spatial coordinate transformations. Writing $p^{ij}=\pi^{ij}/\sqrt h$ avoids ambiguities about covariant derivatives of <tensor densities>.