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

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.

arXiv comment(v1) 16 pages, no figure; (v2) 9 pages, no figure. Compactified for "2012 Awards for Essays on Gravitation" promoted by Gravity Research Foundation. References are deleted. no ingredients is changed. This version received Honorable Mention for 2012

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Cited by in corpus (6)

• Recursive structure in the definitions of gauge-invariant variables for any order perturbations
• Proposal of a gauge-invariant treatment of l=0,1-mode perturbations on Schwarzschild Background Spacetime
• Second-order Gauge-invariant Cosmological Perturbation Theory: Current Status updated in 2019
• Conditions for equivalence of static spherically symmetric spacetimes to almost Friedman-Robertson-Walker
• 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