The space of light rays \({\mathcal {N}}\) of a conformal Lorentz manifold \((M,{\mathcal {C}})\) is, under some topological conditions, a manifold whose basic elements are unparametrized null geodesics. This manifold \({\mathcal {N}}\), strongly inspired on R. Penrose’s twistor theory, keeps all information of M and it could be used as a space complementing the spacetime model. In the present review, the geometry and related structures of \({\mathcal {N}}\), such as the space of skies \(\varSigma \) and the contact structure \({\mathcal {H}}\), are introduced. The causal structure of M is characterized as part of the geometry of \({\mathcal {N}}\). A new causal boundary for spacetimes M prompted by R. Low, the L-boundary, is constructed in the case of 3–dimensional manifolds M and proposed as a model of its construction for general dimension. Its definition only depends on the geometry of \({\mathcal {N}}\) and not on the geometry of the spacetime M. The properties satisfied by the L–boundary \(\partial M\) permit to characterize the obtained extension \({\overline{M}}=M\cup \partial M\) and this characterization is also proposed for general dimension.

共形洛伦兹流形\((M,{\mathcal {C}})\)的光线空间\({\mathcal {N}}\)在某些拓扑条件下是基本元素未参数化的流形零测地线。这个流形\({\mathcal {N}}\)受到 R. Penrose 的扭量理论的强烈启发，保留了M的所有信息，它可以用作补充时空模型的空间。在本综述中，\({\mathcal {N}}\)的几何和相关结构，例如天空空间\(\varSigma \)和接触结构\({\mathcal {H}}\) , 介绍。M的因果结构被表征为几何的一部分\({\mathcal {N}}\)。时空M的新因果边界由 R. Low 提出，L边界是在 3 维流形M的情况下构建的，并被提议作为其一般维度构建的模型。它的定义仅取决于\({\mathcal {N}}\)的几何形状，而不取决于时空M的几何形状。L边界\(\partial M\)满足的性质允许表征获得的扩展\({\overline{M}}=M\cup \partial M\)，并且这种表征也被提出用于一般维度。