Use the <Minkowski metric> $\eta=\operatorname{diag}(1,-1,-1,-1)$ and coordinates $x^0=ct$. At a point, a smooth path is timelike if its tangent $\dot x$ is a <timelike vector>, here meaning $\eta_{ab}\dot x^a\dot x^b>0$. It is lightlike if its tangent is a <null vector>: the same expression is zero and the tangent is nonzero. In these coordinates, a future-directed timelike tangent has spatial speed less than $c$; a lightlike tangent has speed $c$.

Solution

Past exam of the short options course of the University of Oxford / 2023 / 8 / a / i / Solution

 Solution (source code)