Constructing balanced equations of motion for particles in general relativistic theories: the general case

We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. Our approach defines a model for particle like objects which emphasizes different aspects of a set of gravitating objects; by concentrating in the main contributions coming from back reaction effects due to gravitational radiation.