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

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 dieomorphisms for space-times of any dimension m 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.