If you add time coordinates to the spatial coordinates, can there be a circular motion in SpaceTime? That one simplifies a lot to me, so I'm curious to if you agree with me in you needing all coordinates to define a position relative the observer.

There are no circles

instead we find 'spirals'. Also, how would a Lorentz contraction be described in such a 'motion', would it crack up the spinning wheel or not. And think of a planet from this. Wouldn't every point in that planet would then describe a 'spiral'?

How about a sphere, 'free falling' (no acceleration) and being at rest with you. There every point would follow a 'straight line', if we define the 'straightest lines' as those described by geodesics. But if it was rotating in some direction, whilst still being at rest with you, 'free falling'?

How would each point of that ball then look, counting in all coordinates, spatial and time.

==

Alternatively, assume a ring spinning, at rest with you, free falling. Then assume that we rotate the ring, 90 degrees at a time, all directions possible, what would that do to the coordinates, graphically.