The Quasi-Maxwellian Equations of General Relativity: Applications to the Perturbation Theory

TL;DR

This paper reviews the quasi-Maxwellian formalism in general relativity, emphasizing its gauge independence and applicability to cosmological perturbation analysis, offering advantages over traditional methods.

Contribution

It provides a comprehensive overview of the QM formalism and demonstrates its effectiveness in analyzing cosmological perturbations with gauge-independent quantities.

Findings

QM formalism uses gauge-independent quantities

It simplifies the analysis of cosmological perturbations

It offers advantages over traditional gauge-dependent methods

Abstract

A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is made. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lema\^itre-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge independent quantities. We shall see that in the QM-scheme we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz et al that deals with perturbation in the standard Einstein framework. For completeness, we compare the QM-scheme to the gauge-independent method of Bardeen, a procedure consisting on particular choices of the perturbed variables as a combination of gauge dependent quantities.