3 years ago

# L-extensions and L-boundary of conformal spacetimes

A. Bautista, A. Ibort, J. Lafuente

### Abstract

The notion of L-boundary, a new causal boundary proposed by R. Low based on constructing a ‘sky at infinity’ for any light ray, is discussed in detail. The analysis of the notion of L-boundary will be done in the 3-dimensional situation for the ease of presentation. The proposed notion of causal boundary is intrinsically conformal and, as it will be proved in the paper, under natural conditions provides a natural extension $${\overline{M}}$$ of the given spacetime M with smooth boundary $$\partial M = {\overline{M}} {\backslash } M$$ . The extensions $${\overline{M}}$$ of any conformal manifold M constructed in this way are characterised exclusively in terms of local properties at the boundary points. Such extensions are called L-extensions and it is proved that, if they exist, they are essentially unique. Finally it is shown that in the 3-dimensional case, any L-extension is equivalent to the canonical extension obtained by using the L-boundary of the manifold.

DOI: 10.1007/s10714-018-2479-9

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