Constructing balanced equations of motion for particles in general relativity: the null gauge case

TL;DR

This paper introduces a null gauge in general relativity that links the asymptotic and interior structures, enabling the derivation of balanced equations of motion for particles up to second order in acceleration.

Contribution

It develops a null gauge framework that simplifies constructing balanced equations of motion and connects the field equations directly to particle dynamics in general relativity.

Findings

Balanced equations of motion derived up to second order in acceleration.

Null gauge links asymptotic and interior spacetime structures.

Method can be extended to higher orders.

Abstract

We present a convenient null gauge for the construction of the balanced equations of motion. This null gauge has the property that the asymptotic structure is intimately related to the interior one; in particular there is a strong connexion between the field equation and the balanced equations of motion. We present the balanced equations of motion in second order of the acceleration. We solve the required components of the field equation at their respective required orders, $G^2$ and $G^3$. We indicate how this approach can be extended to higher orders.