What Distinguishes Timelike from Non-Spacelike Curves in Spacetime?

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Timelike curves are paths in spacetime where the tangent vector is always timelike, indicating that they represent the trajectory of an object moving slower than light. Non-spacelike curves encompass both timelike and null curves, meaning their tangent vectors can be either timelike or null at different points. This distinction allows for the inclusion of paths that may represent light-like travel alongside slower-than-light trajectories. The key difference lies in the nature of the tangent vectors along the curves. Understanding this differentiation is crucial for analyzing the structure of spacetime.
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Hello,

What is the difference between a timelike and a non-spacelike curve ?
Is it only that "non-spacelike" includes timelike and null curves, or is there another difference ?

Thanks a lot for your help.
 
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emma83 said:
Hello,

What is the difference between a timelike and a non-spacelike curve ?
Is it only that "non-spacelike" includes timelike and null curves, or is there another difference ?

Thanks a lot for your help.

A nonspacelike can include curves whose tangent vector at each point is "either timelike or null" (not just "always timelike" or "always null").
 

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