I review Lorentzian causality theory paying particular attention to the optimality and generality of the presented results. I include complete proofs of some foundational results that are otherwise difficult to find in the literature (e.g. equivalence of some Lorentzian length definitions, upper semi-continuity of the length functional, corner regularization, etc.). The paper is almost self-contained thanks to a systematic logical exposition of the many different topics that compose the theory. It contains new results on classical concepts such as maximizing curves, achronal sets, edges, horismos, domains of dependence, Lorentzian distance. The treatment of causally pathological spacetimes requires the development of some new versatile causality notions, among which I found particularly convenient to introduce: biviability, chronal equivalence, araying sets, and causal versions of horismos and trapped sets. Their usefulness becomes apparent in the treatment of the classical singularity theorems, which is here considerably expanded in the exploration of some variations and alternatives.

我回顾了洛伦兹因果关系理论，特别关注所提出结果的最优性和普遍性。我提供了一些基本结果的完整证明，这些结果很难在文献中找到（例如，一些洛伦兹长度定义的等价性、长度泛函的上半连续性、角正则化等）。由于对构成该理论的许多不同主题进行了系统的逻辑阐述，本文几乎是独立的。它包含经典概念的新结果，例如最大化曲线、非时间集、边缘、horismos、依赖域、洛伦兹距离。处理因果病态时空需要发展一些新的多功能因果关系概念，其中我发现特别方便引入：双生性、时间等价性、araying集以及因果版本的horismos和陷阱集。它们的用处在处理经典奇点定理时变得显而易见，在探索一些变体和替代方案时，奇点定理得到了相当大的扩展。