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It is shown that every stable free t t -homotopy class of closed timelike curves in a compact Lorentzian manifold contains a longest curve which must be a closed timelike geodesic. This result enables one to obtain a Lorentzian analogue of a classical theorem of Synge. A criterion for stability is presented, and a theorem of Tipler is derived as a special case of the result stated above.
Gregory J. Galloway (Sun,) studied this question.
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