MG11 
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Second and higher-order perturbations of a spherical spacetime

We construct a coordinate-invariant framework to deal with arbitrary high-order perturbations of a spherical spacetime and study the issue of gauge invariance. It can be regarded as the generalization to high orders of the Gerlach and Sengupta (GS) formalism for first-order nonspherical perturbations. The GS harmonics are generalized to an arbitrary number of indices and a closed formula is given for their products. Focusing on second-order perturbation theory, we compute all the evolution equations, as well as the equations of perturbed energy-momentum conservation. The framework has been implemented in a computer algebra system specially designed for abstract tensor calculations, what allows us to manipulate the large expressions involved in perturbation theory. So it is ready to be applied to physical problems of interest.