General formulation of general-relativistic higher-order gauge-invariant perturbation theory

Abstract: Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. After reviewing the general framework of the second-order gauge-invariant perturbation theory, we show the fact that the linear-order metric perturbation is decomposed into gauge-invariant and gauge-variant parts, which was the important premis of this general framework. This means that the development the higher-order gauge-invariant perturbation theory on generic background spacetime is possible. A remaining issue to be resolve is also disscussed.