Modified geodesic equations of motion for compact bodies in alternative theories gravity

We derive exact, modified geodesic equations for a system of non-spinning, self-gravitating interacting bodies in class alternative theories gravity to general relativity. use prescription proposed by Eardley incorporating the effects self-gravity within gravitationally bound bodies, which their masses may depend on invariant quantities constructed from auxiliary scalar, vector or tensor fields introduced such theories, evaluated vicinity each body. The forms are independent field chosen theory. In case where strictly constant, reduce conventional These be useful tools deriving motion compact high post-Newtonian orders gravity.