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\[N_{\alpha}=(N_U, -1, -h'(z)/F_z, -\bar{h'}(\bar{z})/F_{\bar{z}})\]

$n^{\alpha}=(0,1,0,0)$

$N^U=1/2G(r)$.
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$F=F(V, z, \bar{z})=V(1-\Omega(z,\bar{z})$;
$\Omega$ can be expressed in terms of $h$ etc. 
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