= Affine rescaling of a null normal
{title2=$\nabla_KK=\kappa K,\quad K(\log h)=-\kappa$}
If a <null vector> tangent satisfies $\nabla_KK=\kappa K$, then $U=hK$ is affine when $K(\log h)=-\kappa$. Choose $h=1$ on the initial transverse surface. The <screen-space projector> kills derivative terms proportional to $K$, so the initial <optical tensor> and its <null expansion> agree with those of $K$. In ingoing spherical coordinates, $K=\partial_v+(f/2)\partial_r$ has $\kappa=f'/2$.
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