Integration of Einstein's Equations in the Weak Field Domain Using the "Einstein" Gauge

TL;DR

This paper introduces a novel gauge for Einstein's equations that simplifies their integration in weak gravitational fields, highlighting the Newtonian potential's role, demonstrated through simple astrophysical models.

Contribution

The paper proposes a new gauge alternative to de Donder gauge, enabling straightforward integration of Einstein's equations in weak fields, with explicit calculations for astrophysical models.

Findings

Simplified integration of Einstein's equations in weak fields.

New role identified for the Newtonian potential.

Explicit solutions demonstrated for astrophysical models.

Abstract

We propose a new alternative gauge for the Einstein equations instead of the de Donder gauge, which allows in the limit of weak fields a straightforward integration of these equations. The Newtonian potential plays a new interesting role in this framework. The calculations are demonstrated explicitely for 2 simple astrophysical models.