7.0 The Geometry of World-Lines

We are now in a position to describe more precisely the world-line of
particles and light rays.

Consider a curve in space-time, \ie, a smooth mapping $\gamma:I\to M$,
where $I$ is some open interval of the real line.  Then, for each number
$\gamma$ in $I$, the tnagent vector to this curve, $\xi^a$, is a
contravariant vector at the point $\gamma(\lambda)$ of $M$.

This curve is said to be timelike if, for each value of $\lambda$,
the tangenet vector $\xi^a$ is timelike; null if, for each $\lambda$,
$\xi^a$ is non-zero and null; and spacelike if, for each $\lambda$,
$]xi^a$ is spacelike.  (Note: timelike and spacelike imply non-zero.)


