Short note on construction of gauge-invariant variables of linear 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 with ADM decomposition, facilitating higher-order gauge-invariant perturbation theory development.

Contribution

It provides an explicit construction of gauge-invariant variables for linear metric perturbations on general backgrounds, advancing the framework for higher-order perturbation analysis.

Findings

Explicit decomposition of metric perturbations into gauge-invariant parts.

Framework for developing higher-order gauge-invariant perturbation theory.

Assumptions enabling explicit construction of gauge-invariant variables.

Abstract

An outline of a proof of the decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on an arbitrary background spacetime which admits ADM decomposition is briefly discussed. We explicitly construct the gauge-invariant and gauge-variant parts of the linear metric perturbations based on some assumptions. This implies that we can develop the higher-order gauge-invariant perturbation theory on an arbitrary background spacetime.