General relativistic forces in non-static spacetimes

The pseudo-Newtonian (ψN) force was defined as the General Relativistic analogue of the Newtonian gravitational force for static spacetimes. It corresponds to the force in a Fermi-normal frame. The extended ψN(eψN) force for non-static spacetimes gives the ψN force in the static spacetime and an expression for the force in some non-static spacetimes. In particular, it gives an exact formula for the momentum imparted to test particles by gravitational waves. However, the frame used for the eψN force was not identified. Here we review the developments of the ψN and eψN formalism and some recent work reducing the apparent arbitrariness in the choice of frame. Some open problems are identified.