Hamiltonian Reduction of Einstein's Equations without Isometries

I apply the Hamiltonian reduction procedure to general spacetimes of 4 dimensions with no isometrics in the (2+2) formalism and find privileged spacetime coordinates. Physical time is chosen as the area element of the two dimensional cross-section of null hypersurfaces. The physical spatial coordinates are defined by equipotential surfaces on a given spacelike hypersurface of constant physical time. The physical Hamiltonian is manifestly local and positive-definite in the privileged coordinates. The complete set of Hamilton's equations is presented and it is found that they coincide with the Einstein's equations written in the privileged coordinates. This shows that the Hamiltonian reduction is a self-consistent procedure.