Abstract
We construct a covariant and gauge-invariant framework to deal with arbitrary high-order perturbations of a spherical spacetime. It can be regarded as the generalization to high orders of the Gerlach and Sengupta formalism for first-order nonspherical perturbations. The Regge-Wheeler-Zerilli harmonics are generalized to an arbitrary number of indices and a closed formula is deduced for their products. An iterative procedure is given in order to construct gauge-invariant quantities up to any perturbative order. Focusing on second-order perturbation theory, we explicitly compute the sources for the gauge invariants as well as for the evolution equations.
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