Perturbation of junction condition and doubly gauge-invariant variables

TL;DR

This paper develops a doubly covariant perturbation scheme for junction conditions in general relativity, enabling gauge-invariant analysis of perturbations in symmetric backgrounds, including brane-world cosmology.

Contribution

It introduces a general doubly covariant perturbation framework for junction conditions, applicable to symmetric backgrounds and useful for brane-world cosmology.

Findings

Derived perturbation equations in doubly gauge-invariant form

Applied the scheme to symmetric backgrounds with constant curvature

Facilitated analysis of cosmological perturbations in brane-world models

Abstract

The junction condition across a singular surface in general relativity, formulated by Israel, has double covariance. In this paper, a general perturbation scheme of the junction condition around an arbitrary background is given in a doubly covariant way. After that, as an application of the general scheme, we consider perturbation of the junction condition around a background with the symmetry of a $(D-2)$-dimensional constant curvature space, where $D$ is the dimensionality of the spacetime. The perturbed junction condition is written in terms of doubly gauge-invariant variables only. Since the symmetric background includes cosmological solutions in the brane-world as a special case, the doubly gauge-invariant junction condition can be used as basic equations for perturbations in the brane-world cosmology.