= Affine parameter change under conformal rescaling
{title2=$d\widetilde\tau/d\tau=C\Lambda^2$}
If $\widetilde g=\Lambda^2g$, a <null geodesic> with <affine parameter> $\tau$ for $g$ has <affine parameter> $\widetilde\tau$ for $\widetilde g$ when $d\widetilde\tau/d\tau=C\Lambda^2$ along the curve. Indeed the <conformal change of the Levi-Civita connection> gives $\widetilde\nabla_VV=2V(\log|\Lambda|)V$; rescaling $V$ by $d\tau/d\widetilde\tau$ cancels this tangential acceleration. Constant $C>0$ preserves the direction of parametrization. Agreement of unparametrized <null geodesics> does not imply agreement of their <affine parameters> or completeness.
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