The space of light rays: Causality and $L$-boundary

Abstract

The space of light rays N of a conformal Lorentz manifold (M, C) is, under some topological conditions, a manifold whose basic elements are unparametrized null geodesics. This manifold N , strongly inspired on R. Penrose's twistor theory, keeps all information of M and it could be used as a space complementing the spacetime model. In the present review, the geometry and related structures of N , such as the space of skies Σ and the contact structure H, are introduced. The causal structure of M is characterized as part of the geometry of N . A new causal boundary for spacetimes M prompted by R. Low, the L-boundary, is constructed in the case of 3-dimensional manifolds M and proposed as a model of its construction for general dimension. Its definition only depends on the geometry of N and not on the geometry of the spacetime M . The properties satisfied by the L-boundary ∂M permit to characterize the obtained extension M = M ∪ ∂M and this characterization is also proposed for general dimension.