论文标题
l延伸和l束相结合的时间
L-extensions and L-boundary of conformal spacetimes
论文作者
论文摘要
详细讨论了L-Boundary的概念，是R-Boundary的一个新因果关系。低于R. Low基于为任何光线构建“无限的天空”的概念。 L-BONDARY概念的分析将在3维情况下进行，以易于表现。所提出的因果边界的概念本质上是保形的，正如本文所证明的那样，在自然条件下提供了自然的扩展$ \ bar {m} $的$ \ bar {m} $，具有光滑边界$ \ partial m = \ bar {m} \ backslash m $。以这种方式构建的任何共形歧管$ m $的扩展名$ \ bar {m} $仅根据边界点的本地属性来表征。这样的扩展称为l扩展，可以证明，如果存在，它们本质上是独一无二的。最后，结果表明，在3维情况下，任何L扩展都等于使用歧管的L边界所获得的规范扩展。
The notion of L-boundary, a new causal boundary proposed by R. Low based on constructing a `sky at infinity' for any light ray, is discussed in detail. The analysis of the notion of L-boundary will be done in the 3-dimensional situation for the ease of presentation. The proposed notion of causal boundary is intrinsically conformal and, as it will be proved in the paper, under natural conditions provides a natural extension $\bar{M}$ of the given spacetime $M$ with smooth boundary $\partial M = \bar{M} \backslash M$. The extensions $\bar{M}$ of any conformal manifold $M$ constructed in this way are characterised exclusively in terms of local properties at the boundary points. Such extensions are called L-extensions and it is proved that, if they exist, they are essentially unique. Finally it is shown that in the 3-dimensional case, any L-extension is equivalent to the canonical extension obtained by using the L-boundary of the manifold.
