# 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 $(X,g)$ a Lorentzian spacetime, a tangent vector $v \in T_x X$ is called

• timelike if $g(v,v) \lt 0$;

• lightlike if $g(v,v) = 0$;

• spacelike if $g(v,v) \gt 0$.

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

Revised on October 30, 2013 22:23:47 by Urs Schreiber (82.169.114.243)