 Solution

On the equatorial plane, the only potentially relevant angular connection coefficient is ${\Gamma }_{\varphi \varphi }^{\theta }=-\sin \theta \cos \theta$, which vanishes at $\theta =\pi /2$. The $\theta$ transport equation is consequently $d{s}^{\theta }/dt=0$. Since the initially radial spin has $s^{\theta }(0)=0$,