In the page http://en.wikiped [Broken]
ia.org/wiki/Hamilton%E2%80%93Jacobi%E2%80%93Einstein_equation, under Shortcomings of four-dimensional spacetime", you can see the following line:

Is it correct?

If it is, how can it be? Because in GR, gravity is space-time curvature!!!

You can have how fields interact in a given curved spacetime.
You cannot solve for that spacetime (in order to let the metric be a dynamical variable).