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Institute for Mathematical Physics 2+1 Sector of 3+1 Gravity 2+1 Sector of 3+1 Gravity

The rank-2 sector of classical 3 + 1 dimensional Ashtekar gravity is considered. It is found that the consistency of the evolution equations with the reality of the volume requires that the 3-surface of initial data is foliated by 2-surfaces tangent to degenerate triads. In turn, the degeneracy is preserved by the evolution. The 2-surfaces behave like 2 + 1 dimensional empty spacetimes with a massless complex eld propagating along each of them. The results provide some evidence for the issue of evolving a non-degenerate gravitational eld into a degenerate sector of Ashtekar's phase space.