Spatial projector of a timelike congruence
= Spatial projector of a timelike congruence
{title2=$h_{ab}=g_{ab}+u_au_b$}
For a unit timelike vector field $u^au_a=-1$, the tensor $h_{ab}=g_{ab}+u_au_b$ projects onto the three-dimensional subspace orthogonal to $u^a$. In particular, $h_{ab}u^a=h_{ab}u^b=0$ and $g^{ab}h_{ab}=3$ in four spacetime dimensions.