High-order gauge-invariant perturbations of a spherical spacetime

Details High-order gauge-invariant perturbations of a spherical spacetime High-order gauge-invariant perturbations of a spherical spacetime

2007-03-12

arxiv.org/abs/gr-qc/0703069v1

Phys.Rev.D76:024004,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.1103/PhysRevD.76.024004

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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