A conformal boundary for space-times based on light-like geodesics: the 3-dimensional case

Abstract

A new causal boundary, which we will term the $l$-boundary, inspired by the geometry of the space of light rays and invariant by conformal diffeomorphisms for space-times of any dimension $m\ge 3$, proposed by one of the authors (R.J. Low, The space of null geodesics (and a new causal boundary), Lecture Notes in Physics, 692, Springer, 2006, 35--50) is analyzed in detail for space-times of dimension 3. Under some natural assumptions it is shown that the completed space-time becomes a smooth manifold with boundary and its relation with Geroch-Kronheimer-Penrose causal boundary is discussed. A number of examples illustrating the properties of this new causal boundary as well as a discussion on the obtained results will be provided.

28 pages, 5 figures

References in corpus (3)

• Globally hyperbolic spacetimes can be defined as "causal" instead of "strongly causal"
• Linking and causality in globally hyperbolic spacetimes
• Causality and skies: is non-refocussing necessary?

Cited by in corpus (1)

• L-extensions and L-boundary of conformal spacetimes