The Causal Boundary of spacetimes revisited

Abstract

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 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.

arXiv comment37 pages, 10 figures; Definition 6.1 slightly modified; multiple minor changes; one figure added and another replaced

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• On Conformal Infinity and Compactifications of the Minkowski Space
• Isocausal spacetimes may have different causal boundaries
• The Attached Point Topology of the Abstract Boundary For Space-Time
• Functors in Lorentzian geometry -- three variations on a theme
• Minimal Elements of the Causal Boundary with Applications to Spacetime Splitting
• The Strongly Attached Point Topology of the Abstract Boundary For Space-Time
• Isometries of spacetimes without observer horizons