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

DOI10.1007/S10714-022-02942-3arXiv2206.04964MaRDI QIDQ6401667

A. Bautista, Alberto Ibort, J. Lafuente

Publication date: 10 June 2022

Abstract: The space of light rays $mathcalN$ of a conformal Lorentz manifold $(M,mathcalC)$ is, under some topological conditions, a manifold whose basic elements are unparametrized null geodesics. This manifold $mathcalN$, 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 $mathcalN$, such as the space of skies $Sigma$ and the contact structure $mathcalH$, are introduced. The causal structure of $M$ is characterized as part of the geometry of $mathcalN$. 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 $mathcalN$ and not on the geometry of the spacetime $M$. The properties satisfied by the $L$-boundary $partialM$ permit to characterize the obtained extension $overlineM=McuppartialM$ and this characterization is also proposed for general dimension.

Mathematics Subject Classification ID

Relativistic cosmology (83F05) Quantum optics (81V80) Boundary element methods applied to problems in optics and electromagnetic theory (78M15) Electromagnetic fields in general relativity and gravitational theory (83C50) Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism (83C60) Contact manifolds (general theory) (53D10) Conformal structures on manifolds (53C18) Causal inference from observational studies (62D20)

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