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Short note on construction of gauge-invariant variables of linear metric perturbations on an arbitrary background spacetime

An outline of a proof of the decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on an arbitrary background spacetime which admits ADM decomposition is briefly discussed. We explicitly construct the gauge-invariant and gauge-variant parts of the linear metric perturbations based on some assumptions. This implies that we can develop the higher-order gauge-invariant perturbation theory on an arbitrary background spacetime.

preprint2011arXivOpen access
Kouji Nakamura
astro-ph.COmath-phmath.MPgr-qchep-th
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Kouji Nakamura

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