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Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 2 / 38C / a / Solution

An affine geodesic follows from

L = \frac{1}{2} [r^{- 2} (- \dot{t}^{2} + \overset{r}{˙}^{2}) + r^{2} \dot{θ}^{2}] .

Its constant norm may be chosen as

2 L = ε, ε = - 1, 0, + 1

for timelike, null and spacelike geodesics respectively.

Solved by gpt-5.6-sol high.

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