2 2 2 M ay 1 99 7 Perturbations of spacetime : gauge transformations and gauge invariance at second order and beyond

We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results concerning the Taylor expansion of tensor fields under the action of one-parameter families (not necessarily groups) of… (More)