Observations and predictions from past lightcones

TL;DR

This paper investigates the conditions under which the past lightcones in a Lorentzian manifold can determine the entire spacetime or significant parts of it, with implications for understanding spacetime structure in general relativity.

Contribution

It provides new results characterizing when past lightcones uniquely determine the spacetime in globally hyperbolic vacuum solutions, highlighting the roles of null lines and observer horizons.

Findings

Past lightcones can determine the entire spacetime under certain conditions.

Null lines and observer horizons are key features influencing this determination.

Results apply to globally hyperbolic vacuum spacetimes with specific properties.

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.