Construction of gauge-invariant variables for linear-order metric
  perturbations on some background spacetimes
  Gauge-invariant treatments of general-relativistic higher-order perturbations
on generic background spacetime is proposed. We show the fact that the
linear-order metric perturbation is decomposed into gauge-invariant and
gauge-variant parts, which was the important premise of this general framework.
This means that the development the higher-order gauge-invariant perturbation
theory on generic background spacetime is possible.
