Timelike curve

A timelike curve has a nonzero tangent vector with negative Minkowski norm in metric signature $(-,+,+,+)$ at every regular point. A physical massive observer's world line is also future-directed. Parametrizing it by coordinate time gives $-c^2+|\mathbf{v}{|}^2<0$, or $|\mathbf{v}|<c$: the local tangent condition is exactly the subluminal speed condition. It is stronger than checking only that two endpoints have timelike separation.