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arXiv · 1311.2986

The Framework, Causal and Co-compact Structure of Space-time

Martin Kovár·Alena Chernikava
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Abstract

We introduce a canonical, compact topology, which we call weakly causal, naturally generated by the causal site of J. D. Christensen and L. Crane, a pointless algebraic structure motivated by certain problems of quantum gravity. We show that for every four-dimensional globally hyperbolic Lorentzian manifold there exists an associated causal site, whose weakly causal topology is co-compact with respect to the manifold topology and vice versa. Thus, the causal site has the full information about the topology of space-time, represented by the Lorentzian manifold. In addition, we show that there exist also non-Lorentzian causal sites (whose causal relation is not a continuous poset) and so the weakly causal topology and its de Groot dual extends the usual manifold topology of space-time beyond topologies generated by the traditional, smooth model. As a source of inspiration in topologizing the studied causal structures, we use some methods and constructions of general topology and formal concept analysis.

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Martin Kovár, Alena Chernikava. 2013-11-13. The Framework, Causal and Co-compact Structure of Space-time. https://arxiv.org/abs/1311.2986

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