(In)Stability of solitons and black holes in Anti-de Sitter

Anti-de Sitter (AdS) as well as asymptotically AdS (aAdS) space-times have gained lots of interest recently, mainly due to the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. Since the boundary of AdS - unlike that of Minkowski space-time - is time-like, important differences appear. In this talk, I will discuss globally regular as well as black hole solutions in gravity models with minimally coupled scalar fields. I will put the emphasize on the discussion of the (in)stabilities of these solutions, which have interesting interpretations on the (strongly coupled) CFT side.