General formulation of general-relativistic higher-order gauge-invariant perturbation theory

TL;DR

This paper develops a comprehensive framework for higher-order gauge-invariant perturbation theory in general relativity, enabling more accurate analysis of perturbations on complex spacetimes.

Contribution

It introduces a general formulation for higher-order gauge-invariant perturbations, building on the decomposition of linear perturbations into gauge-invariant and gauge-variant parts.

Findings

Decomposition of linear metric perturbations into gauge-invariant and gauge-variant components.

Framework for extending gauge-invariant perturbation theory to higher orders.

Discussion of unresolved issues in the development of the theory.

Abstract

Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. After reviewing the general framework of the second-order gauge-invariant perturbation theory, we show the fact that the linear-order metric perturbation is decomposed into gauge-invariant and gauge-variant parts, which was the important premis of this general framework. This means that the development the higher-order gauge-invariant perturbation theory on generic background spacetime is possible. A remaining issue to be resolve is also disscussed.