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 Quote by George Jones $$n^a n^b h_{ab}=?$$
$$n^a n^b h_{ab}=0$$
 Quote by George Jones Now suppose $v^a$ is orthogonal to $n^a$. $$v^a v^b h_{ab}=?$$
$$v^a v^b h_{ab}=v^a v^b g_{ab}$$

Now choose an othonormal that has $n^a$ as one element. What does the matrix for $h$ with respect to this basis look like?