In a general Lorentzian manifold M, the past lightcone of a point is a proper subset of M that does not carry enough information to determine the rest of M. In special circumstances however, say if M is a globally hyperbolic Cauchy development of vacuum initial data on a Cauchy surface S and there is a point whose past lightcone contains S, then the contents of such a lightcone does determine M up to isometry. We present results that describe what properties of M guarantee that past lightcones do indeed determine all or at least significant portions of M. Null lines and observer horizons, which are well known features of the de-Sitter spacetime, play a prominent role.

在一般的洛伦兹流形M 中，一个点的过去光锥是M 的一个真子集，它没有携带足够的信息来确定M的其余部分。然而，在特殊情况下，假设M是柯西表面S上真空初始数据的全局双曲柯西展开，并且有一个点的过去光锥包含S，那么这样的光锥的内容确实确定了M直到等距。我们提供的结果描述了M 的哪些特性保证过去的光锥确实决定了M 的全部或至少重要部分. 作为去西特时空的众所周知的特征，零线和观察者视界发挥着重要作用。