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IOP Publishing, Classical and Quantum Gravity, 3(24), p. 745-749

DOI: 10.1088/0264-9381/24/3/n01

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Globally hyperbolic spacetimes can be defined as "causal" instead of "strongly causal"

Journal article published in 2006 by Antonio N. Bernal, Miguel Sánchez ORCID
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This paper is available in a repository.

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Abstract

The classical definition of {\em global hyperbolicity} for a spacetime $(M,g)$ comprises two conditions: (A) compactness of the diamonds $J^+(p)∩ J^-(q)$, and (B) strong causality. Here we show that condition (B) can be replaced just by causality. In fact, we show first that the classical definition of causal simplicity (which impose to be distinguishing, apart from the closedness of $J^+(p)$, $J^-(q)$) can be weakened in causal instead of distinguishing. So, the full consistency of the causal ladder (recently proved by the authors in a definitive way) yields directly the result. ; Comment: 5 pages, no figures, latex. This paper includes the results concerning global hyperbolicity in previous gr-qc/0610136 (which will be withdrawn)