Obtaining General Relativity's N‐body non‐linear Lagrangian from iterative, linear algebraic scaling equations

Abstract

AbstractA 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 its 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 exterior effacement along with needed metric potential expansions. Then additional properties of gravity – interior effacement and Lorentz time dilation and spatial contraction – produce additional iterative, linear algebraic equations for obtaining the full non‐linear and motion‐dependent N‐body gravity Lagrangian potentials as well. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)