The space of light rays: Causality and L–boundary

Abstract

The space of light rays {mathcal {N}} of a conformal Lorentz manifold (M,{mathcal {C}}) is, under some topological conditions, a manifold whose basic elements are unparametrized null geodesics. This manifold {mathcal {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 {mathcal {N}}, such as the space of skies varSigma and the contact structure {mathcal {H}}, are introduced. The causal structure of M is characterized as part of the geometry of {mathcal {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 {mathcal {N}} and not on the geometry of the spacetime M. The properties satisfied by the L–boundary partial M permit to characterize the obtained extension {overline{M}}=Mcup partial M and this characterization is also proposed for general dimension.