Constructing metric gravity's N-body non-linear Lagrangian from iterative, linear algebraic scaling equations

TL;DR

This paper introduces an iterative linear algebraic method to construct the N-body Lagrangian in metric gravity, enforcing invariance properties and deriving the full Schwarzschild metric potentials.

Contribution

It presents a novel iterative algebraic approach to derive the N-body Lagrangian in metric gravity, including the full Schwarzschild metric potentials.

Findings

Derived the 1/c^4 order N-body Lagrangian.

Constructed Schwarzschild temporal and spatial metric potentials.

Demonstrated enforcement of invariance properties in gravity.

Abstract

A method for constructing metric gravity's N-body Lagrangian is developed which uses iterative, liner algebraic euqations which enforce invariance properties of gravity --- exterior effacement, interior effacement, and the time dilation and Lorentz contraction of matter under boosts. The method is demonstrated by obtaining the full 1/c^4 order Lagrangian, and a combination of exterior and interior effacement enforcement permits construction of the full Schwarzschild temporal and spatial metric potentials.