Construction of gauge-invariant variables for linear-order metric perturbations on some background spacetimes
Kouji Nakamura
备注：
4 pages, no figure, Prepared for the proceedings of 20th Workshop On General Relativity and Gravitation (Sept. 21 - Sept. 25, (2010), YITP Kyoto University, Japan)
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.
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.
An outline of a proof of the decomposition of the linear metric perturbation into gauge-invariant and gauge-variant parts on an arbitrary background spacetime is discussed through an exlicit construction of gauge-invariant and gauge-variant parts. Although this outline is incomplete, yet, due to our assumptions, we propose a conjecture which states that the linear metric perturbation is always decomposed into its gauge-invariant and gageu-variant parts. If this conjecture is true, we can develop the higher-order gauge-invariant perturbation theory on an arbitrary background spacetime.
An outline of a proof of the decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on the an arbitrary background spacetime which admits ADM decomposition is discussed. We explicitly construct the gauge-invariant and gauge-variant parts of the linear metric perturbations through the assumption of the existence of some Green functions. We also confirm the result through another approach. This implies that we can develop the higher-order gauge-invariant perturbation theory on an arbitrary background spacetime. Remaining issues to complete the general-framework…
The decomposition of the linear-order metric perturbation is discussed in the context of the higher-order gauge-invariant perturbation theory. We show that the linear order metric perturbation is decomposed into gauge-invariant and gauge-variant parts on the general background spacetime which admits ADM decomposition. This decomposition was an important premise of the general framework of the higher order gauge-invariant perturbation theory proposed in the papers [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723; ibid. vol.113 (2005), 481]. This implies that we can develop the higher-order …
Construction of the gauge-invariant variables for the linear metric perturbation, which was proposed in the paper [K. Nakamura, arXiv:1101.1147], is discussed through an alternative approach. Our starting point of the construction of the gauge-invariant variables is an non-trivial non-local decomposition of the linear metric perturbation. Assuming the existence of some Green functions, we reproduce results in the above paper. This supports the consistency of the result and implies that one can develop the general-relativistic higher-order gauge-invariant perturbation theory on general backgrou…
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Metric Reconstruction and Second Order Perturbation for Generic Spherically Symmetric spacetime
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学学院，UCAS）；University of Chinese Academy of Sciences（中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
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