**Previous section: ****Defining Spacetime****.**

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Spacetime maps are essential for physical interpretation of GA equations in relativity theory.

This is a spacetime map showing the lightcone for an event *X*_{0} . Events *X** _{k} *(

*k*= 1, 2, 3) lie on straight lines passing through

*X*

_{0}. Displacements

*∆*

*X*

*=*

_{k}*X*

*−*

_{k}*X*

_{0}are said to be

*or*

**timelike**,**lightlike**,**, respectively, as they lie inside, on, or outside the invariant lightcone.**

*spacelike*This is a spacetime map of events in a timelike plane showing the position vector **x **= *X*_{2} − *X*_{1} for the event *X *= *ct *+ **x **with respect to a given inertial system.

A differentiable curve in spacetime is said to be timelike, lightlike, or spacelike if its tangent is proportional to, respectively, a timelike, lightlike, or spacelike displacement.

__Previous section__**: ****Defining Spacetime****.**

**Next section: ****Particle History and Proper Velocity****.**