  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 $m\geq 3$, 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.
