Approximation Method for the Relaxed Covariant Form of the Gravitational Field Equations for Particles

TL;DR

This paper develops a covariant approximation method for the relaxed form of Einstein's gravitational field equations, specifically tailored for analyzing particles, and extends existing results to a coordinate-free framework.

Contribution

It introduces a covariant decomposition approach to the relaxed Einstein equations and applies it to particle analysis up to second order, generalizing previous results.

Findings

Generalized known results to a coordinate-free covariant form

Developed an approximation method for particles in relaxed field equations

Applied the method to analyze particles up to second order

Abstract

We present a study of the so called relaxed field equations of general relativity in terms of a decomposition of the metric; which is designed to deal with the notion of particles. Several known results are generalized to a coordinate free covariant discussion. We apply our techniques to the study of a particle up to second order.