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The formulations of Regge-discretised general relativity which are analogous to the tetrad and self-dual representations of the continuum theory are studied.

We investigate whether self-maintained vacuum traversible wormhole can exist described by stationary but nonstatic metric. We consider metric being the sum of static spherically symmetric one and a small nondiagonal component which describes rotation sufficiently slow to be taken into account in the linear approximation. We study semiclassical Einstein equations for this metric with vacuum expectation value of stress-energy of physical fields as the source. In suggestion that the static traversible wormhole solution exists we reveal possible azimuthal angle dependence of angular velocity of the rotation (angular velocity of the local inertial frame) that solves semiclassical Einstein equations. We find that in the macroscopic (in the Plank scale) wormhole case a rotational solution exists but only such that, first, angular velocity depends on radial coordinate only and, second, the wormhole connects the two asymptotically flat spacetimes rotating with angular velocities different in asymptotic regions.

Regge calculus is considered as a particular case of the more general system where the linklengths of any two neighbouring 4-tetrahedra do not necessarily coincide on their common face. This system is treated as that one described by metric discontinuous on the faces. In the superspace of all discontinuous metrics the Regge calculus metrics form some hypersurface. Quantum theory of the discontinuous metric system is assumed to be fixed somehow in the form of quantum measure on (the space of functionals on) the superspace. The problem of reducing this measure to the Regge hypersurface is addressed. The quantum Regge calculus measure is defined from a discontinuous metric measure by inserting the $\delta$-function-like phase factor. The requirement that this reduction would respect natural physical properties (positivity, well-defined continuum limit, absence of lattice artefacts) put rather severe restrictions and allows to define practically uniquely this phase factor.Comment: 8 pages, LaTe