Truncation of Einstein equations through Gravitational Foliation

In previous works we suggested to consider a (3 + 1)D quantum
gravitational field as an “evolution” of a (2 + 1)D renormalized quan-
tum gravitational field along the direction of the gravitational force.
The starting point of the suggestion is derivation of a unique hyper-
surface which looks effectively like (2 + 1)D from the point of view of
Einstein equations in (3 + 1)D. In this paper we derive such unique
hypersurfaces for different kinds of stationary spherical metrics. We
find that these hypersurfaces exist whenever all the components of the
gravitational force field vanish on the hypersurface. We discuss the
implication of this result and the necessary further work.