Gauge-invariant variables in general-relativistic perturbations: globalization and zero-mode problem

TL;DR

This paper discusses the decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts in general relativity, highlighting the zero-mode problem's role in globalizing this decomposition and advancing higher-order perturbation theory.

Contribution

It provides an explicit construction of gauge-invariant variables and addresses the zero-mode problem for globalizing metric perturbation decomposition.

Findings

Explicit construction of gauge-invariant variables

Identification of the zero-mode problem as essential for globalization

Implication for higher-order gauge-invariant perturbation theory

Abstract

An outline of a proof of the local decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on an arbitrary background spacetime is briefly explained. We explicitly construct the gauge-invariant and gauge-variant parts of the linear metric perturbations based on some assumptions. We also point out the zero-mode problem is an essential problem to globalize of this decomposition of linear metric perturbations. The resolution of this zero-mode problem implies the possibility of the development of the higher-order gauge-invariant perturbation theory on an arbitrary background spacetime in a global sense.