Landau, in his Classical Theory of Fields Textbook remarks (while explaining GR) that a rotating disc viewed from an inertial frame of reference will no longer remain euclidean since the periphery will lorentz contract while the radius will remain same and therefore, the c/d ratio will be less than pi. I have two confusions here:
GR says that geometry is coordinate invariant, then how can this be true?
The disc is rotating and therefore is an accelerating frame of reference, then how can we speak of lorentz contraction since that would mean we are relating distances in one inertial frame to distances in another inertial frame via a lorentz transformation but the disc frame is not inertial?
