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I just wanted to verify if my intuitive understanding of why space time (if it is to be physically plausible) can not be compact.

According to Hawking and Ellis (and others) space time can not be compact because it would allow for the existence of closed time like curves. I understand (I think) that argument based on limit points, or accumulation points, which define a (sequence) compact space and how this allows such curves to exist.

Now, is it also correct, and much simpler, to assume that *if* space time was compact, this would imply "special" points in space time (i.e. the limit points) which breaks the principle of relativity, somehow...?

I.e. if space time is compact, then there exists an arbitrary number of points which are the accumulation points for sequences of time like curves and (ignoring *completely* the closed-timelike curve problem) this would imply that geodesics would be influenced by other things than just mass/energy (as the causal argument is independent of any solution to Einstein's field equations.)

Or am I very very far off on a tangent indeed..?