Extremal Higher Spin Black Holes

Understand

The gauge sector of three-dimensional higher spin gravities can be formulated as a Chern-Simons theory.

• In this context, a higher spin black hole corresponds to a flat connection with suitable holonomy (smoothness) conditions which are consistent with the properties of a generalized thermal ensemble.
• Building on these ideas, we discuss a definition of black hole extremality which is appropriate to the topological character of 3d higher spin theories.
• Our definition can be phrased in terms of the Jordan class of the holonomy around a non-contractible (angular) cycle, and we show that it is compatible with the zero-temperature limit of smooth black hole solutions.