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arXiv · 2207.01273

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

A. Bautista·A. Ibort·J. Lafuente·R. Low
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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 $m\geq 3$, 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.

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A. Bautista, A. Ibort, J. Lafuente, R. Low. 2022-07-04. A conformal boundary for space-times based on light-like geodesics: the 3-dimensional case. https://doi.org/10.1063/1.4976506

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