Construction of gauge-invariant variables for linear-order metric perturbations on some background spacetimes

TL;DR

This paper develops a framework for gauge-invariant linear perturbations in general relativity, enabling higher-order perturbation analysis on generic backgrounds by decomposing metric perturbations into gauge-invariant and gauge-variant parts.

Contribution

It introduces a method to decompose linear-order metric perturbations into gauge-invariant and gauge-variant components, foundational for higher-order gauge-invariant perturbation theory.

Findings

Linear-order metric perturbation decomposed into gauge-invariant and gauge-variant parts

Framework enables higher-order gauge-invariant perturbation analysis

Supports generic background spacetimes

Abstract

Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. We show the fact that the linear-order metric perturbation is decomposed into gauge-invariant and gauge-variant parts, which was the important premise of this general framework. This means that the development the higher-order gauge-invariant perturbation theory on generic background spacetime is possible.