论文标题
因果关系简单的空间空间空间上的接触结构
The contact structure on the space of null geodesics of causally simple spacetimes
论文作者
论文摘要
结果表明，Minkowski空间的星形因果关系子集的无效测量空间是与$ \ Mathbb {r}^n $的球形cotangent束中的规范接触结构的接触型。在$ 3 $维的情况下，我们证明了大量全球双曲线时空的可因果关系合理的子集的结果相似，从接触率表面的理论中采用方法。此外，我们证明，在某些假设下，具有光滑边界的因果简单时空嵌入的无效的空间，进入全球双曲线时空的无效测量空间。该边界的特征性叶面提供了因果简单时空的共形类别的不变。
It is shown that the space of null geodesics of a star-shaped causally simple subset of Minkowski space is contactomorphic to the canonical contact structure in the spherical cotangent bundle of $\mathbb{R}^n$. In the $3$-dimensional case we prove a similar result for a large class of causally simple contractible subsets of an arbitrary globally hyperbolic spacetime applying methods from the theory of contact-convex surfaces. Moreover we prove that under certain assumptions the space of null geodesics of a causally simple spacetime embeds with smooth boundary into the space of null geodesics of a globally hyperbolic spacetime. The characteristic foliation of this boundary provides an invariant of the conformal class of the causally simple spacetime.
