Minkowski spacetime the has a flat metric of Lorentzian signature (-1,1,1,1).
It is well known (c.f. Geroch 1967 & citation there) that whether a manifold admits a metric of Lorentzian signature is equivalent to the question of whether it admits a nowhere vanishing timelike vector field. By Geroch's theorem the spacelike hypersurfaces of Minkowski spacetime are diffeomorphic to each other, the diffeomorphism being produced by the integral curves of such a timelike vector field.
Since the metric on each spacelike slice of Minkowski spacetime is the (flat) Euclidean metric, the diffeomorphism must be an isometry, but among the possible isometries are rotations.
Question: is there any sense to the idea any each slice may be related another by a rotation? What physical or mathematical justification would there be for [disallowing] allowing such diffeomorphisms? (If the timelike vector field had curl, could one have a corkscrew hole in ~Minkowski space?)
The independent rotation of spatial hypersurfaces being something like this...