Nonlinear perturbations of higher dimensional anti-de Sitter spacetime

TL;DR

This paper investigates nonlinear gravitational perturbations of higher-dimensional anti-de Sitter spacetime, extending previous work for four dimensions, and analyzes the resonant structure at second order in five dimensions.

Contribution

It generalizes the analysis of nonlinear perturbations to higher dimensions and examines the resonance phenomena in five-dimensional AdS spacetime.

Findings

Resonant terms vanish at second order for studied cases

Tensor perturbations are a new feature in higher dimensions

Asymptotic AdS conditions achieved through gauge choices

Abstract

We study nonlinear gravitational perturbations of vacuum Einstein equations, with $\Lambda<0$ 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. The tensor perturbations are the new feature of higher dimensions. We render the metric perturbations asymptotically anti-de Sitter by employing a suitable gauge choice for each of the sectors. 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.