When Rindler co-ordinates are drawn why are accelerated obserevers drawn in an area implying faster than light motion?

Question

When using Rindler co-ordinates, the motion of accelerated objects is drawn on the right hand side of a light cone. See the image in the "Characteristics of a Rindler Frame" section in this wikipedia article with the pink lines:https://en.wikipedia.org/wiki/Rindler_coordinates

But when I learned special relativity I learned that if something is moving in that area to the right of the light cone, then it's moving faster than light.

Please help me make sense why the hyperbolas are drawn in that part of the space in order to study accelerated observers when it seems to permit faster than light motion?

I feel like they should be drawn and studied inside the light cone instead, so clearly I'm misunderstanding something.

Answer 1

There is no specifically forbidden "region" in a real spacetime diagram in SR.

If you look at the accelerated world line, it starts nearly vertical, and "tilts" over as speed increases, but never gets to less than 45 degrees (which would indicate FTL).

So there is no problem. Does that help?.