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 , 1 propagates to increasing values of for perturbations of higher order, owing to mode coupling. We also discuss in which circumstances it is possible to construct the invariants.
- Received 12 March 2007
DOI:https://doi.org/10.1103/PhysRevD.76.024004
©2007 American Physical Society