There are many questions on the Ehrenfest paradox but I couldn't find a duplicate (which may stil exist).
The rim of a rotating disc would be Lorentz-contracted as seen from a non-rotated observer but the radius would not. I visualize this using a number of equidistant points on the rim of the disc making up a regular polygon. The requirement that the sides are (Lorentz-) contracted implies that the radius must be contracted as well.
I assume that the solutions in general relativity has to do with the gravitational-equivalent centrifugal force. Light from the rim would appear gravitationally red-shifted as seen from the center, and it perhaps contracts the radius as well. I am aware that for example Wikipedia’s explanations, or suggested solutions, seem much more complicated.
Based on this reasoning, my question is now: Surely, this effect would apply to a rotating ring with no material present except for that which makes up the ring which might be taken to be (almost) arbitrarily thin - and the central observer.
So why does material science and Born rigidity make its way into the paradox?