MG13 proceedings: Construction of gauge-invariant variables for linear-order metric perturbations on an arbitrary background spacetime

TL;DR

This paper discusses a method to decompose linear metric perturbations into gauge-invariant and gauge-variant parts on arbitrary backgrounds, proposing a conjecture that could enable higher-order gauge-invariant perturbation theory development.

Contribution

It provides an explicit construction and outline for decomposing metric perturbations, proposing a conjecture for a general decomposition applicable to arbitrary backgrounds.

Findings

Proposed a conjecture for metric perturbation decomposition.

Outlined an explicit construction method.

Discussed implications for higher-order perturbation theory.

Abstract

An outline of a proof of the decomposition of the linear metric perturbation into gauge-invariant and gauge-variant parts on an arbitrary background spacetime is discussed through an exlicit construction of gauge-invariant and gauge-variant parts. Although this outline is incomplete, yet, due to our assumptions, we propose a conjecture which states that the linear metric perturbation is always decomposed into its gauge-invariant and gageu-variant parts. If this conjecture is true, we can develop the higher-order gauge-invariant perturbation theory on an arbitrary background spacetime.