nLab
timelike curve

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Differential geometry

differential geometry

synthetic differential geometry

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Riemannian geometry

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theory (physics), model (physics)

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Gravity

Contents

Definition

For (X,g)(X,g) a Lorentzian spacetime, a tangent vector vT xXv \in T_x X is called

  • timelike if g(v,v)<0g(v,v) \lt 0;

  • lightlike if g(v,v)=0g(v,v) = 0;

  • spacelike if g(v,v)>0g(v,v) \gt 0.

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

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