Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 309 / 1 / e / Solution

For a radial null geodesic, $k=0$ gives ${\dot{r}}^2=e^2$. Choose the affine parameter so that $r(0)=0$ and the outgoing branch has $\dot{r}=e>0$. ThenUsing $dr/d\lambda =e$,Consequently $r\to \infty$ whileThe conformal boundary is infinitely far away in affine parameter but is reached in finite static coordinate time.