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

4 pages, no figure. (v3) some explanations are added and a reference is added

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Cited by in corpus (7)

• Construction of gauge-invariant variables of linear metric perturbations on an arbitrary background spacetime
• Proposal of a gauge-invariant treatment of l=0,1-mode perturbations on Schwarzschild Background Spacetime
• Gauge-invariant variables in general-relativistic perturbations: globalization and zero-mode problem
• Recursive structure in the definitions of gauge-invariant variables for any order perturbations
• Post-linear metric of a compact source of matter
• Comparing a gauge-invariant formulation and a "conventional complete gauge-fixing approach" for $l=0,1$ mode perturbations on the Schwarzschild background spacetime
• Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part I : -- Formulation and odd-mode perturbations