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

Under parallel transport, the gyroscope spin obeys $u^b{\nabla }_b{s}^a=0$, and its freely falling circular orbit is a geodesic, $u^b{\nabla }_b{u}^a=0$. Metric compatibility therefore givesThus $s^a{u}_a$ is constant along the orbit.