Communications in Mathematical Physics

, Volume 276, Issue 3, pp 611–643 | Cite as

The Causal Boundary of Spacetimes Revisited

  • José L. Flores


We present a new development of the causal boundary of spacetimes, originally introduced by Geroch, Kronheimer and Penrose. Given a strongly causal spacetime (or, more generally, a chronological set), we reconsider the GKP ideas to construct a family of completions with a chronology and topology extending the original ones. Many of these completions present undesirable features, like those which appeared in previous approaches by other authors. However, we show that all these deficiencies are due to the attachment of an “excessively big” boundary. In fact, a notion of “completion with minimal boundary” is then introduced in our family such that, when we restrict to these minimal completions, which always exist, all previous objections disappear. The optimal character of our construction is illustrated by a number of satisfactory properties and examples.


Ideal Point Causal Structure Timelike Curve Minkowski Plane Conformal Boundary 
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© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Departamento de Álgebra, Geometría y Topología, Facultad de CienciasUniversidad de MálagaMálagaSpain

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