The centrifugal force can be arbitrary small. Say that we have only the outer rim of the pie, but as large as a galaxy. The centrifugal force at the half of speed of light is just negligible. Far less than all the everyday centrifugal forces we deal with.
Now say, that the rim has a zero around velocity at first and we are watching it from the centrer. Gradually, say in a million years time, it accelerates to a relativistic speed. The forces associated are a millionth of Newton per kilogram of mass. No big deal.
The problem is only this - where's the Lorentz contraction?
As long as we have only one spaceship orbiting the Galaxy, we can imagine this Lorentzian shrinking. In the case of that many, that they are all around, we can't.
The problem is only this - where's the Lorentz contraction?
Each piece of the ring is longer as measured by an inertial observer comoving with it than as measured by a stationary one (i.e. one comoving with the centre of the ring). But note that there's no inertial observer that's comoving with all pieces of the ring at the same time, and if you add the length of each piece as measured by an observer comoving with it what you're measuring is not a closed curve, it's a helix in spacetime. (I will draw a diagram when I have time if I remember to.)
As per a recent comment this thread is meant to voice contrarian opinions, that is anything this community tends not to agree with. Thus I ask you to post your contrarian views and upvote anything you do not agree with based on personal beliefs. Spam and trolling still needs to be downvoted.