In a <coordinate basis>, parallel transport is
$$
\frac{ds^\mu}{d\tau}+\Gamma^\mu_{\rho\nu}\frac{dx^\rho}{d\tau}s^\nu=0.
$$
Along the circular orbit, $dr=d\theta=0$ and $d\phi/dt=\Omega$. Dividing by $dt/d\tau$ gives
$$
\boxed{\frac{ds^\mu}{dt}+\Gamma^\mu_{t\nu}s^\nu
+\Omega\Gamma^\mu_{\phi\nu}s^\nu=0}.
$$

Solution

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

 Solution

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