Nonlinear perturbations of higher dimensional anti–de Sitter spacetime

Abstract

We study nonlinear gravitational perturbations of vacuum Einstein equations, with Λ<0 in (n+2) dimensions, with n>2, generalizing previous studies for n = 2. We follow the formalism by Ishibashi, Kodama, and Seto to decompose the metric perturbations into tensor, vector, and scalar sectors, and simplify the Einstein equations. We study, for the first time, general tensor perturbations. We render the metric perturbations in each sector asymptotically anti–de Sitter. Finally, we analyze the resonant structure of the perturbed equations at second order for the five dimensional case, by a partial study of single mode tensor-type perturbations at the linear level. For the cases we studied, resonant terms vanish at second order.