Timelike curve
= 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>.