 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-4/37a/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

A radial timelike geodesic has conserved

E = f \dot{t}

and normalization

\overset{r}{˙}^{2} = E^{2} - f

. Choose

E > 1

and the outward sign. Then

Δ τ = \int_{0}^{b} \frac{d r}{E ^{2} - 1 + r ^{2} / b ^{2}} < \infty,

so the observer reaches

r = b

in finite proper time even though static coordinate

t

diverges.

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