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Sorry, I do realize that this is probably a really stupid question, but can someone please help me understand the following statement:
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.
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.
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.
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.
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.