Almost all extremal AdS black holes are singular

If asymptotically anti-de Sitter (AdS) boundary conditions break spherical symmetry, the behavior of static extremal black holes is very different from the familiar Reissner-Nordstrom AdS solution. In four dimensions, almost all black holes become singular in the extremal limit. The singularity is a weak null singularity in which the metric is continuous but tidal forces diverge on the event horizon. Surprisingly, the singularity is stronger for larger black holes. In five dimensions, if one breaks SO(4) symmetry (but preserves SO(3)), there is a new extremal black hole with a near horizon geometry that is a warped product of AdS2 and a deformed three-sphere. These results affect black hole thermodynamics and have implications for the IR behavior of holographic theories. (Based on joint work with Maciek Kolanowski and Jorge Santos.)