  We study the metastability of Anti-de Sitter topological black holes with
compact hyperbolic horizons. We focus on the five-dimensional case, an AdS/CFT
dual to thermal states in the maximally supersymmetric large-N Yang-Mills
theory, quantized on a three-dimensional compact hyperboloid. We estimate the
various rates for quantum-statistical D3-brane emission, using WKB methods in
the probe-brane approximation, including thermal tunneling and Schwinger pair
production. The topological black holes are found to be metastable at high
temperature. At low temperatures, D-branes are emitted without exponential
suppression in superradiant modes, producing an instability in qualitative
agreement with expectations from weakly-coupled gauge dynamics.
