Short note on 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 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.

4 pages, no figures, jgrg21.sty is used. Prepared for the proceedings of the International Conference JGRG21 (2011, Sendai, Japan)