SEMICLASSICAL INTERPRETATION OF THE TOPOLOGICAL SOLUTIONS FOR CANONICAL QUANTUM-GRAVITY

Ashtekar's formulation for canonical quantum gravity is known to posse ss the topological solutions which have their support only on the modu li space N of flat SL(2,C) connections. We show that each point on the moduli space N corresponds to a geometric Structure, or more precisel y the Lorentz group part of a family of Lorentzian structures,on the f lat (3+1)-dimensional spacetime. A detailed analysis is given in the c ase where the spacetime is homeomorphic to RxT(3). Most of the points on the moduli space N yield pathological spacetimes which suffer from singularities on each spatial hypersurface or which violate the strong causality condition. There is, however, a subspace of N on which each point corresponds to a family of regular spacetimes.