Initially $s^a$ is radial, whereas the circular-orbit four-velocity has only $t$ and $\phi$ components. The diagonal <Schwarzschild metric> therefore gives $s^au_a=0$ at $t=0$. By part i,
$$
\boxed{s^au_a=0}
$$
throughout the orbit.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 309 / 1 / a / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-309/1/a/ii/solution