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My understanding of a timelike path, is one which always stays inside a light cone, defined by lines with gradients c and -c that cross at the origin.My GR notes said:[For a given metric] ...t is timelike and x spacelike for x > 2m, their roles are swapped for 0 < x < 2m.

This means that the region x > 2m is time-reversal invariant – taking t → −t the pattern of

possible trajectories are the same.

However, for 0 < x < 2m, where x plays the role of ‘time’, we must choose between time

running from left to right, i.e. with increasing x, or from right to left, i.e. with decreasing x.

What does it mean to say that time coordinate

**itself**is timelike or spacelike (and the same for space-coordinates?) And what does it mean to say "x plays the role of time".

Thanks.