Can General Relativity's N-Body Lagrangian Be Obtained from Iterative Algebraic Scaling Equations? I. Exterior Effacement

A local system of bodies in General Relativity whose exterior metric field asymptotically approaches the Minkowski metric effaces any effects of the matter distribution exterior to the Minkowski boundary condition. To enforce to all orders this property of gravity which appears to hold in nature, a method using linear algebraic scaling equations is developed, which generates by an iterative process an N-body Lagrangian expansion for gravity's motion-independent potentials, which fulfills the exterior effacement. The algebraic method is then applied in this first of two papers to produce the motion-independent N-body gravity Lagrangian to the 1/c(4) order of expansion. A subsequent paper supplements exterior effacement conditions with others-interior effacement and Lorentz time dilation and spatial contraction- to create additional iterative algebraic equations for obtaining the nonlinear, motion-dependent N-body gravity Lagrangian potentials as well. The scaling conditions developed in these papers may also serve as validation checks on more traditional determinations of higher-order gravity which employ perturbative solutions of gravity's nonlinear field equations.