= Galilean spacetime
{c}
{title2=$(M,t_a,h^{ab},\nabla)$}
A geometric background for <Newtonian mechanics> consisting of a four-dimensional <affine space>, an absolute time covector $t_a$, a rank-three positive spatial inverse <metric tensor> $h^{ab}$ with $t_ah^{ab}=0$, and a flat torsion-free <affine connection> preserving both. A trajectory parametrized by absolute time has tangent $u$ with $t_a u^a=1$. Its absolute <acceleration> is $\nabla_u u$; an unforced particle obeys $\nabla_u u=0$. The structure distinguishes <inertial motion> without selecting an absolute state of uniform rest. Additional force laws, including a Newtonian gravitational force when wanted, specify a dynamical theory on this background.
Back to article page
