= Inertial motion
{title2=$\nabla_u u=0$}
Motion with zero <acceleration> relative to the theory's inertial <affine connection>. In an <inertial frame>, its spatial trajectory is uniform and straight. The geometric statement refers to the connection, not to a chosen <coordinate system>; force-free motion supplies its physical interpretation. In <general relativity> the corresponding freely falling trajectories are <timelike geodesics>, with local inertial coordinates rather than a global <inertial frame> in a curved region.
Back to article page
