Can General Relativity’s N-body Lagrangian be obtained from iterative algebraic scaling equations? II. Interior effacement and time dilation

Abstract

In the companion paper [1], iterative algebraic scaling equations were developed which yield motion-independent potentials to all non-linear orders for gravity’s N-body Lagrangian which enforce exterior effacement—that local gravity expressed in local proper coordinates is not affected by the distribution of matter in the universe exterior and far from the local system of bodies. This paper deals with determination of the motion-dependent potentials of gravity’s N-body Lagrangian. Additional algebraic scaling conditions are developed for this purpose which exploit other invariances desired for gravity—that a local gravitational system must have dynamics which manifest Lorentz time dilation and spatial contractions upon boosts and does not reveal a preferred inertial frame in the cosmos; and additionally, for composite body sources, interior effacement is enforced in which only a single total mass-energy parameter represents the body in its spherical limit in all N-body Lagrangian potentials. Iterative algebraic equations for enforcing these conditions as well as the exterior effacement condition are applied to obtain a 1/c 4 order N-body Lagrangian for gravity.