Construction of gauge-invariant variables of linear metric perturbation on general background spacetime

Details Construction of gauge-invariant variables of linear metric perturbation on general background spacetime Construction of gauge-invariant variables of linear metric perturbation on general background spacetime

2011-05-20

arxiv.org/abs/1105.4007v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 pages, no figure. Compacted version of arXiv:1101.1147v1[gr-qc] but includes new ingredients

Scientific paper

It is shown that the linear order metric perturbation is decomposed into gauge-invariant and gauge-variant parts on the general background spacetime which admits ADM decomposition. 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 generic background spacetime. Remaining issues to complete the general-framework of the higher-order gauge-invariant perturbation theories are also discussed.

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