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High-order gauge-invariant perturbations of a spherical spacetime

David Brizuela·Jose M. Martin-Garcia·Guillermo A. Mena Marugan
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Abstract

We complete the formulation of a general framework for the analysis of high-order nonspherical perturbations of a four-dimensional spherical spacetime by including a gauge-invariant description of the perturbations. We present a general algorithm to construct these invariants and provide explicit formulas for the case of second-order metric perturbations. We show that the well-known problem of lack of invariance for the first-order perturbations with l=0,1 propagates to increasing values of l for perturbations of higher order, owing to mode coupling. We also discuss in which circumstances it is possible to construct the invariants.

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David Brizuela, Jose M. Martin-Garcia, Guillermo A. Mena Marugan. 2007-03-12. High-order gauge-invariant perturbations of a spherical spacetime. https://doi.org/10.1103/physrevd.76.024004

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