nLab
timelike curve

Definition

For $(X,g)$ a Lorentzian spacetime, a tangent vector $v\in T_{x}X$ is called

• timelike if $g(v,v)<0$;

• lightlike if $g(v,v)=0$;

• spacelike if $g(v,v)>0$.

A curve $\gamma :ℝ\to X$ is called timelike or lightlike or spacelike if all of its tangent vectors $\dot{\gamma }$ are, respectively.

Related concepts

• future cone

• Lorentzian spacetime