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arXiv · 1306.4927

Generalized Formalism in Gauge-Invariant Gravitational Perturbations

Rong-Gen Cai·Li-Ming Cao
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Abstract

By use of the gauge-invariant variables proposed by Kodama and Ishibashi, we obtain the most general perturbation equations in the $(m+n)$-dimensional spacetime with a warped product metric. These equations do not depend on the spectral expansions of the Laplace-type operators on the $n$-dimensional Einstein manifold. These equations enable us to have a complete gauge-invariant perturbation theory and a well-defined spectral expansion for all modes and the gauge invariance is kept for each mode. By studying perturbations of some projections of Weyl tensor in the case of $m=2$, we define three Teukolsky-like gauge-invariant variables and obtain the perturbation equations of these variables by considering perturbations of the Penrose wave equations in the $(2+n)$-dimensional Einstein spectime. In particular, we find the relations between the Teukolsky-like gauge-invariant variables and the Kodama-Ishibashi gauge-invariant variables. These relations imply that the Kodama-Ishibashi gauge-invariant variables all come from the perturbations of Weyl tensor of the spacetime.

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Rong-Gen Cai, Li-Ming Cao. 2013-06-20. Generalized Formalism in Gauge-Invariant Gravitational Perturbations. https://doi.org/10.1103/physrevd.88.084047

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