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Physics
Special and General Relativity
Rindler Wedge: Timelike or Spacelike? Intuition & Light Cone
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[QUOTE="PeterDonis, post: 6626942, member: 197831"] If this is your intuition then your intuition needs to be retrained. It makes no sense to say a region of spacetime is "timelike" or "spacelike"; those terms only make sense for worldlines or vectors. You might be thinking of integral curves of the "boost" Killing vector field in Minkowski spacetime, which are timelike hyperbolas in the Rindler wedge but are spacelike hyperbolas above the future horizon or below the past horizon. However, those are curves, not regions. I think what you are trying to say here is that, if we look at curves passing through the origin of Minkowski coordinates, timelike curves lie inside the light cone, null curves lie on the light cone, and spacelike curves lie outside the light cone. That is correct. However, this has nothing whatever to do with worldlines in the Rindler wedge, since none of those worldlines pass through the origin. There are timelike worldlines in the Rindler wedge (i.e., the region of spacetime with ##x > 0## and ##|t| < x##) that stay in that wedge forever, and there are other timelike worldlines in that wedge that enter the wedge from below the past Rindler horizon (the line ##t = -x##) and/or exit the wedge to above the future Rindler horizon (the line ##t = x##). But those worldlines stay timelike everywhere regardless of their behavior relative to the wedge and its boundaries. [/QUOTE]
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Special and General Relativity
Rindler Wedge: Timelike or Spacelike? Intuition & Light Cone
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