nLab timelike curve

Context

Differential geometry

differential geometry

synthetic differential geometry

Applications

Riemannian geometry

Riemannian geometry

Surveys, textbooks and lecture notes

Gravity

gravity, supergravity

Contents

Definition

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

• timelike if $g\left(v,v\right)<0$;

• lightlike if $g\left(v,v\right)=0$;

• spacelike if $g\left(v,v\right)>0$.

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

Created on May 16, 2011 17:31:36 by Urs Schreiber (131.211.238.144)