Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 37A / c / Solution

A radial timelike geodesic has conserved $E=f\dot{t}$ and normalization ${\dot{r}}^2=E^2-f$. Choose $E>1$ and the outward sign. Thenso the observer reaches $r=b$ in finite proper time even though static coordinate $t$ diverges.