Abstract

AdS is one of the three vacuum solutions to General Relativity and, as such, the natural question to ask is whether it is stable or not. Although the other two vacuum solutions, namely Minkowski and de Sitter spaces, were proven long ago to be non-linearly stable, a similar study had not taken place for AdS until a few years ago. The first model developed to study this problem was that of a perturbation of AdS in the form of a spherically symmetric, massless scalar field. One then traces the evolution of the scalar field to see whether it collapses to form a Black Hole, or the perturbation remains small for ever. Although initially it was conjectured that AdS is generically unstable, later developments on the subject revealed a large class of perturbations that do not collapse, raising in this way questions about the initial conjecture. In this talk, I will review the model of spherical symmetric perturbations in AdS explaining at the same time the underlying dynamics, I will refer to both numerical and analytic results and I will try to explain the phase space of solutions in the limit where the amplitude of the perturbation vanishes.