Hamiltonian reduction of Einstein’s equations without isometries

I apply the Hamiltonian reduction procedure to 4-dimensional spacetimes without isometries and find privileged spacetime coordinates in which the physical Hamiltonian is expressed in terms of the conformal two metric and its conjugate momentum. Physical time is the area element of the cross section of null hypersurface, and the physical radial coordinate is defined by equipotential surfaces on a given spacelike hypersurface of constant physical time. The physical Hamiltonian is local and positive in the privileged coordinates. Einstein’s equations in the privileged coordinates are presented as Hamilton’s equations of motions obtained from the physical Hamiltonian.