Revisión de la teoría de perturbaciones en Relatividad General

Abstract

This work presents a review of the different approaches for perturbation theory in General Relativity: the Gauge Invariant formalism, the 1+3 Covariant Gauge Invariant theory and the traditional gauge fixing method. In particular, this review focuses in the Gauge Invariant formalism, due to it has a broader applicability (it applies not only to General Relativity but, to any theory that must fulfill the principle of general covariance) than the other two formalisms and because it has an algorithmic method for calculate the invariant variables to perturbation orders larger than the linear one. The article includes too, a brief discussion about the root of the problem of gauge-invariance in the perturbation theory in General Relativity. To help the reader, this last approach is applied to the cosmological scenario.