Affine momentum normalization of a geodesic
= Affine momentum normalization of a geodesic
For physical <four-momentum> $P^\mu=m\,dx^\mu/d\tau$, the covariant-component equation is $dP_\mu/d\tau=(\partial_\mu g_{\nu\sigma})P^\nu P^\sigma/(2m)$. The equation without $1/m$ instead uses a tangent parametrization, or the <affine parameter> $\lambda=\tau/m$ when the tangent is the physical momentum.