Unstable horizons

We investigate some of the issues relating to the dynamical instability of general static spacetimes with horizons. Our paper will be partially pedagogical and partially exploratory in nature. After discussing the current understanding, we generalize the proposal of Gubser and Mitra, which identifies dynamical instability of black branes with local thermodynamic instability, to include all product spacetimes with the horizon uniformly smeared over an internal space. We support our conjecture by explicitly exhibiting a threshold unstable mode for Schwarzschild-AdS(5) x S-5 black hole. Using the AdS/CFT correspondence, this simultaneously yields a prediction for a phase transition in the dual gauge theory. We also discuss implications for spacetimes with cosmological horizons.