An ensemble of cosmological models based on generalized BFtheory is constructed where the rôle of vacuum (zero-level) coupling constants is played by topologically invariant rational intersection forms (cosmological-constant matrices) of 4-dimensional plumbed Vcobordisms which are interpreted as Euclidean spacetime regions. For these regions describing topology changes, the rational and integer intersection matrices are calculated. A relation is found between the hierarchy of certain elements of these matrices and the hierarchy of coupling constants of the universal (low-energy) interactions.

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We show that all static spherically symmetric spacetimes admit a conformally Kerr - Schild metric representation.

Eigenvectors of stress-energy tensor (the source in Einstein's equations) form privileged bases in description of the corresponding space-times. When one or more of these vector fields are rotating (the property well determined in differential geometry), one says that the space-time executes this rotation. Though the rotation in its proper sense is understood as that of a timelike congruence (vector field), the rotation of a spacelike congruence is not a less objective property if it corresponds to a canonical proper basis built of the just mentioned eigenvectors. In this last case, we propose to speak on pseudo-rotation. Both properties of metric, its material sources, and space-time symmetries are considered in this paper.

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