L-extensions and L-boundary of conformal spacetimes Articles uri icon

publication date

  • December 2018

start page

  • 1

end page

  • 47

issue

  • (153)

volume

  • 50

International Standard Serial Number (ISSN)

  • 0001-7701

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 M¯ of the given spacetime M with smooth boundary ∂M=M¯∖M . The extensions 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.

keywords

  • causal boundary; c-boundary; l-boundary; conformal spacetime