= Scalar momentum constraint with positive extrinsic curvature
{title2=$D_jK^j{}_i-D_iK=\frac2a\partial_i(\psi'+\mathcal H A)$}
For scalar metric potentials $ds^2=a^2[-(1+2A)d\tau^2+2B_{,i}d\tau dx^i+((1-2\psi)\delta_{ij}+2E_{,ij})dx^idx^j]$ and positive <extrinsic curvature>, $\delta K^i{}_j=a^{-1}[-(\psi'+\mathcal HA)\delta^i{}_j+\partial^i\partial_j(E'-B)]$. The scalar shear terms cancel between its divergence and trace gradient. With $j_i=-P^\mu{}_iT_{\mu\nu}n^\nu$, the <momentum constraint> becomes $2\partial_i(\psi'+\mathcal HA)/a=-8\pi G j_i$. Reversing the convention for $K$ reverses the geometric left side.
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