= Null affine parameter under a conformal rescaling
{title2=$d\widetilde\lambda=\Omega^2\,d\lambda$}
If $g$ is rescaled to $\widetilde g=\Omega^2g$, a null geodesic retains its unparametrized path. For its original affine tangent $k$, the changed connection gives $\widetilde\nabla_k k=2k(\log\Omega)k$. Rescaling the tangent by $\Omega^{-2}$ cancels this term and proves the displayed affine-parameter relation, up to a constant multiplier. A conformal boundary may therefore be reached at finite unphysical affine parameter while physical affine parameter is infinite.
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