在一劳仑兹流形中，一条封闭类时曲线（closed timelike curve，CTC）是一物质粒子于时空中的一种世界线，其为「封闭」，亦即会返回起始点。这种可能性是由威廉·范·斯托克姆（Willem Jacob van Stockum）于1937年以及库尔特·哥德尔（Kurt Gödel）于1949年开启研究风潮。若CTC存在，则似乎隐射时间机器理论上可行，如此也引出了祖父悖论（grandfather paradox）的梦魇。CTC与参考系拖曳（frame dragging）以及提普勒柱体（Tipler Cylinder）有关，是广义相对论带来的众多有趣的「副作用」其中一者。

In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime that is "closed", returning to its starting point. This possibility was discovered by Kurt Gödel in 1949, who discovered a solution to the equations of general relativity (GR) allowing CTCs known as the Gödel metric; and since then other GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes. If CTCs exist, their existence would seem to imply at least the theoretical possibility of time travel backwards in time, raising the spectre of the grandfather paradox, although the Novikov self-consistency principle seems to show that such paradoxes could be avoided. Some physicists speculate that the CTCs which appear in certain GR solutions might be ruled out by a future theory of quantum gravity which would replace GR, an idea which Stephen Hawking has labeled the chronology protection conjecture. Others note that if every closed timelike curve in a given space-time passes through an event horizon, a property which can be called chronological censorship, then that space-time with event horizons excised would still be causally well behaved and an observer might not be able to detect the causal violation.