Observations and predictions from past lightcones

Abstract

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. That said, 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 determines all of M (up to isometry). We show some 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.