I'm familiar with how one foliates, say, a four-dimensional spacetime [itex](\mathcal{M},g)[/itex] so that one can identify it as a sequence of spatial hypersurfaces [itex]\mathcal{M}\simeq\Sigma\times I[/itex] where [itex]\Sigma[/itex] is some spatial three-manifold and [itex]I\subseteq\mathbb{R}[/itex]. However, suppose that we're interested in a spacetime which has at least one compact dimension. For clarity, let's look at(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\mathcal{N} \simeq \mathcal{M}\times S^1,[/tex]

i.e., something like a Kaluza-Klein spacetime with one compact periodic dimension per spacetime point. Does anybody know if any work has been done on foliating a spacetime like this into spatial hypersurfaces? Is this even possible?

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# Foliations of spacetime

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