Alternative construction of gauge-invariant variables for linear metric perturbation on general background spacetime

TL;DR

This paper presents an alternative method for constructing gauge-invariant variables in linear metric perturbations on general backgrounds, supporting the development of higher-order gauge-invariant perturbation theory in general relativity.

Contribution

It introduces a non-local decomposition approach for gauge-invariant variable construction, confirming previous results and enabling higher-order perturbation analysis.

Findings

Reproduces previous gauge-invariant variable results

Supports development of higher-order perturbation theory

Validates the non-local decomposition approach

Abstract

Construction of the gauge-invariant variables for the linear metric perturbation, which was proposed in the paper [K. Nakamura, arXiv:1101.1147], is discussed through an alternative approach. Our starting point of the construction of the gauge-invariant variables is an non-trivial non-local decomposition of the linear metric perturbation. Assuming the existence of some Green functions, we reproduce results in the above paper. This supports the consistency of the result and implies that one can develop the general-relativistic higher-order gauge-invariant perturbation theory on general background spacetime.