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.