Higher Order Perturbations Around Backgrounds with One Non-Homogeneous Dimension

TL;DR

This paper demonstrates that perturbations around backgrounds with one non-homogeneous dimension can be systematically simplified to any order, unifying treatments of cosmological and spherically symmetric perturbations, with applications to black strings.

Contribution

It generalizes previous linear results to nonlinear perturbations and provides a canonical simplification method for backgrounds with one non-homogeneous dimension.

Findings

Perturbations can be canonically simplified at all orders in perturbation theory.

The method unifies treatments of cosmological and spherically symmetric backgrounds.

Application to black strings illustrates the approach's utility.

Abstract

It is shown that perturbations around backgrounds with one non-homogeneous dimension, namely of co-homogeneity 1, can be canonically simplified, a property that is shown to hold to any order in perturbation theory. Recalling that the problem naturally reduces to 1d, a procedure is described whereby for each gauge function in 1d two 1d fields are eliminated from the action - one is gauge and can be eliminated without a constraint and the other is auxiliary. These results generalize the results of hep-th/0609001 from linear to non-linear perturbations and they unify two cases of physical interest: cosmological perturbations and perturbations to static spherically symmetric backgrounds. An application to black strings is discussed in some detail.