Instability of anti-de Sitter spacetime.

I will describe recent evidence that anti-de Sitter spacetime is nonlinearly unstable. Generic small but finite perturbations eventually form small black holes. I will also present evidence that there are special solutions, called geons, which remain close to anti-de Sitter. I will argue that one can put black holes inside the geons to obtain a family of black holes in anti-de Sitter spacetime with only one continuous symmetry.