Relativity relatively revisited

A little research into the writings of one of my heroes, Godel, has provided me with an interesting conundrum. I understand general relativity pretty well; well enough that I can manipulate the more simple solutions to the field equations. But I have a problem… or is it physics??

We all remember special relativity and the deductions that distance and time are dependent upon relative motion, and what happens in one frame of reference can be described equally as well in another frame of reference, provided gravity is ignored and the frames are moving in a uniform non-rotating manner. But general relativity elaborates on this, including gravity and any relative motion whatsoever. Just as in special relativity, in general relativity any frame of motion works equally well to describe any motion. Hell, its all relative.
Well, Schwartzchild discovered that there are solutions to the field equations for gravity that would produce infinite gravitation: the Schwartzchild singularity. Then they were observed (black holes, they are called, because Schwartzchild singularity is a mouthful). Also, we can see that because of the distortion that gravity has on the four dimensional spacetime fabric, all bodies move along “geodesics” in space-time – the shortest 4D path geometrically speaking. But if we change frames of reference, we’re okay – ’cause its all relative. Still things move along geodesics – just with regard to the newly distorted space-time. Also, for general relativity to be “true” all imaginable possible “universes” that satisfy the field equations are all equally valid.
But then Godel had to come along. In 1949 he published a brief paper showing solutions to the field equations (now called Godel Universes) where the geodesic was a circle. “A circle!!?” you exclaim. Or perhaps you don’t. This would mean that traveling quickly, one would come to a “point” in “time” that was the beginning. Time would be circular. But before you break out the H. G. Wells, if you go forward to the past, then the past hasn’t passed because it is presently the future. Either it is, or in the Godel Universe, there is no time. “Okay fine, there’s no time in the Godel Universe, so fucking what?” But if in this possible universe there is no time, it is equally valid in all universes satisfying the strictures of general relativity – including our own. Therefore there’s no time.
So, relativity captures time and shoe-horns it into a space-like dimension. This renders all philosophic, empirical, epistemological concerns for time null. But in capturing time, in sealing it with space, in making it computable, time pulled a Houdini – and vanished.
What now?