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 tangential 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 field propagating along each of them. The results provide some evidence for the issue of evolving a non-degenerate gravitational field into a degenerate sector of Ashtekar's phase space.