On the existence of closed timelike geodesics in compact spacetimes (Q1601766)

The existence of closed timelike geodesics is generally believed to lead to problems with causality, and therefore, this topic was of little interest among researchers for a while. The situation changed recently by the observation, that examples exist where those geodesics can be restricted to small microscopically small regions, and in the large, causality will remain intact. The present paper gives a further step towards understanding of space-times possessing such geodesics; especially, if that space-time is compact. Illustrative examples are given showing that compact space-times without closed timelike geodesics can exist, and certain assumptions on Cauchy hypersurfaces are met.