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

Details Gauge-invariant variables in general-relativistic perturbations: globalization and zero-mode problem Gauge-invariant variables in general-relativistic perturbations: globalization and zero-mode problem

2012-03-29

arxiv.org/abs/1203.6448v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, no figure

Scientific paper

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.

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