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arXiv · 2207.01292

L-extensions and L-boundary of conformal spacetimes

A. Bautista·A. Ibort·J. Lafuente
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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 $\bar{M}$ of the given spacetime $M$ with smooth boundary $\partial M = \bar{M} \backslash M$. The extensions $\bar{M}$ 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.

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A. Bautista, A. Ibort, J. Lafuente. 2022-07-04. L-extensions and L-boundary of conformal spacetimes. https://doi.org/10.1007/s10714-018-2479-9

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