First of all, I'm having a difficulty in defining what a static spacetime is. Does it presume that the objects with mass in the system are just sitting around and doing nothing, with no motion, relative to our frame, so there can be no motion and change in curvature of spacetime through time? Secondly, if objects with motion curve space time in a way that they change the curvature along their path, does this also imply that free-falling objecs also curve space time in the same way? Thirdly, in Newtonian physics there is an earth and apple example where Earth also accelerates towards the apple because of the same force with opposite directions. Does the same hold in GR?