Closed timelike geodesics

Abstract

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.