M. Novello, E. Bittencourt, J. M. Salim
Published 2013-02-28Version 1
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.
Comments: The main goal of this review is to make a little more popular the use of the JEK frame in the realm of perturbation theory of Friedman universes. Indeed, the Lifshitz-Bardeen method and the JEK frame give the same results for the perturbations in the linear regime. The main interest on JEK rests on its unambiguous way to deal with perturbation within the cosmological FLRW scenario
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