An investigation of Stability of Anti-de Sitter Spacetime

Abstract

In this project, we analyze the structure of non spherically-symmetric Tensor Gravitational perturbations in the Transverse Traceless(TT) gauge beyond the linearized order on Anti-de Sitter(AdS) background in a generic dimension. The spherical symmetry of the background is used to simplify the perturbation equations. We start with introducing AdS and it’s causal structure, and then review some work on scalar field perturbations which lead to instability in that spacetime in the first chapter. Additionally, we present the calculation for higher order equations for this system. In the second chapter, we derive the dynamical equations of gravitational perturbations in TT gauge upto second order for the given background. After that, a formalism developed in [1] is introduced and applied to simplify the dynamical equations at linear and nonlinear order. Finally, we conclude with the analysis of the structure of second order equations, and its results.