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.

结果表明，Minkowski空间的星型因果简单子集的零大地测量学空间与球面正切束中的正则接触结构是同形的。 ${\mathbb{[R}}^{ñ}$。在3维情况下，我们从接触凸曲面理论中证明了任意全局双曲时空应用方法的一大类因果简单可收缩子集的相似结果。此外，我们证明了在某些假设下，因果简单时空的零地线测绘空间以平滑边界嵌入到全局双曲时空的零地线测绘空间中。该边界的特征性叶面提供了因果简单时空的保形类的不变性。