Assuming a stationary, globally hyperbolic spacetime, I can imagine that all spacelike foliations are topologically equivalent though not all will be identical since the spacetime is not static. Is there a proof of this somewhere? If not, could somebody give me a rigorous argument please?

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    $\begingroup$ I'm afraid not! physics.stackexchange.com/questions/353148/… $\endgroup$
    – Slereah
    Mar 24 '20 at 19:01
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    $\begingroup$ Is the question whether all slices in a spacelike foliation have the same topology, or that the slices of all possible foliations have the same topology? $\endgroup$
    – mmeent
    Mar 24 '20 at 19:09
  • $\begingroup$ @Slereah this is very helpful thank you very much. $\endgroup$
    – Y2H
    Mar 24 '20 at 20:07

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