Spin four-vector
= Spin four-vector
{title2=$s^\mu$}
The spin of a small torque-free test <gyroscope> is represented by a <spacelike vector> orthogonal to its <four-velocity>, $s^\mu u_\mu=0$. Its temporal component vanishes in its own <rest frame>. Along a <geodesic>, $Ds^\mu/d\tau=0$: <parallel transport> preserves the orthogonality and the invariant spin magnitude. For an accelerated observer the corresponding nonrotating transport is <Fermi-Walker transport>.