= Positive-expansion convention for extrinsic curvature
{title2=$K_{\mu\nu}=P^\rho{}_\mu P^\sigma{}_\nu\nabla_\rho n_\sigma$}
With a future unit timelike normal in signature $(-,+,+,+)$, this convention makes the <extrinsic curvature> trace equal to the normal congruence's expansion, $K=\nabla_\mu n^\mu$. An expanding flat <Friedmann-Lemaître-Robertson-Walker metric> has $K_{ij}=a'\delta_{ij}$ and $K=3a'/a^2$. This is the opposite sign to the negative-expansion convention used in many <3+1 decomposition of spacetime> formulas. Projection identities and momentum constraints must use the same convention throughout.
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