The space of light rays: causality and \(L\)-boundary. (English) Zbl 1508.83023
Summary: 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 \(\overline{M}=M\cup\partial M\) and this characterization is also proposed for general dimension.
MSC:
| 83F05 | Relativistic cosmology |
| 53D10 | Contact manifolds (general theory) |
| 78M15 | Boundary element methods applied to problems in optics and electromagnetic theory |
| 53C18 | Conformal structures on manifolds |
| 62D20 | Causal inference from observational studies |
| 81V80 | Quantum optics |
| 83C50 | Electromagnetic fields in general relativity and gravitational theory |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
Keywords:
contact manifold; \(L\)-boundary; conformal manifold; causal structure; light rays; strongly causal spacetimesReferences:
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