论文标题
光线的空间：因果关系和$ l $ boundary
The space of light rays: Causality and $L$-boundary
论文作者
论文摘要
在某些拓扑条件下，光线$ \ Mathcal $ \ Mathcal {n} $ $（M，\ Mathcal {C}）$在某些拓扑条件下是一种歧管，其基本元素是未透明的无否定为null GeoDesics。在R. Penrose的Twistor理论上强烈启发了此歧管$ \ MATHCAL {N} $，保留了$ M $的所有信息，并且可以用作互补时空模型的空间。在本评论中，介绍了$ \ Mathcal {n} $的几何和相关结构，例如天空$σ$和触点结构$ \ Mathcal {H} $。 $ m $的因果结构的特征是$ \ Mathcal {n} $的几何形状的一部分。 $ l $ boundary的R. Low提示的SpaceTimes $ M $的新因果边界是在$ 3 $二维的歧管$ M $的情况下建造的，并建议作为其通用尺寸的构建模型。它的定义仅取决于$ \ Mathcal {n} $的几何形状，而不取决于时空$ m $的几何形状。 $ l $ boundarary $ \ partial m $允许所满足的属性，以表征所获得的扩展名$ \ overline {m} = m \ cup \ partial m $，并且还为一般维度提出了这种表征。
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 $Σ$ 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.
