Construction of gauge-invariant variables of linear metric perturbations on an arbitrary background spacetime

Abstract

An outline of a proof of the decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on the an arbitrary background spacetime which admits ADM decomposition is discussed. We explicitly construct the gauge-invariant and gauge-variant parts of the linear metric perturbations through the assumption of the existence of some Green functions. We also confirm the result through another approach. This implies that we can develop the higher-order gauge-invariant perturbation theory on an arbitrary background spacetime. Remaining issues to complete the general-framework of the general-relativistic higher-order gauge-invariant perturbation theories are also discussed.

26 pages, no figure. Compacted version of arXiv:1101.1147v1[gr-qc] but includes new ingredients; (v2) Title is slightly changed. Some discussions and references are added. Some typos are corrected

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Cited by in corpus (12)

• Gauge invariants of linearized gravity with a general background metric
• Proposal of a gauge-invariant treatment of l=0,1-mode perturbations on Schwarzschild Background Spacetime
• Recursive structure in the definitions of gauge-invariant variables for any order perturbations
• Second-order Gauge-invariant Cosmological Perturbation Theory: Current Status updated in 2019
• Dirac procedure and the Hamiltonian formalism for cosmological perturbations in a Bianchi I universe
• Short note on construction of gauge-invariant variables of linear metric perturbations on an arbitrary background spacetime
• Conditions for equivalence of static spherically symmetric spacetimes to almost Friedman-Robertson-Walker
• Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part II: -- Even-mode perturbations
• 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
• MG13 proceedings: Construction of gauge-invariant variables for linear-order metric perturbations on an arbitrary background spacetime
• Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part III: -- Realization of exact solutions