1203.6448 (Kouji Nakamura)

Gauge-invariant variables in general-relativistic perturbations:
globalization and zero-mode problem    [PDF]

Kouji Nakamura

An outline of a proof of the local 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. We also point out the zero-mode problem is an essential problem to globalize of this decomposition of linear metric perturbation. The resolution of this zero-mode problem implies the possibility of the development of the higher-order gauge-invariant perturbation theory on an arbitrary background spacetime in a global sense.

View original: http://arxiv.org/abs/1203.6448