york Definition and 1 Threads

Using York decomposition as a foundation, can we reformulate General Relativity to treat space as flat (##R_{ij} = 0##), redistributing all curvature into a vector field for time (##\vec{t}_i##)? The York decomposition: $$\tilde{h}_{ij} = \phi^{-4} h_{ij}$$ $$\tilde{K}_{ij} = \phi^2 K_{ij}$$...