3.1 CMC foliations

Note that CMC foliations are unique in cosmological vacuum spacetimes. In the case of vacuum T3-Gowdy, there is a CMC foliation exhausting the interval (− ∞, 0) [49Jump To The Next Citation Point]. However, in the case of S2 × S1 and S3 topology, the only general statements concerning foliations are, as far as we are aware, the ones given in [16Jump To The Next Citation Point]. It is natural to conjecture that if there is a CMC Cauchy hypersurface in the S2 × S1 or S3 case, there is a CMC foliation exhausting the interval (− ∞, ∞ ) [66]. However, to the best of our knowledge there are no results to this effect.
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