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Closed timelike curve
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== Contractible versus noncontractible == There are two classes of CTCs. We have CTCs contractible to a point (if we no longer insist it has to be future-directed timelike everywhere), and we have CTCs which are not contractible. For the latter, we can always go to the [[universal covering space]], and reestablish causality. For the former, such a procedure is not possible. No closed timelike curve is contractible to a point by a [[timelike homotopy]] among timelike curves, as that point would not be causally well behaved.<ref name="monroe"/>
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