Abstract:
The study of higher spin gravity theories has gathered much interest in recent years. In
three dimensions, these theories are particularly tractable due to the fact that they can be
de ned in terms of a Chern-Simons theory. A higher spin black hole then corresponds to a
at connection with appropriate holonomy conditions in this framework. Building on this, we
study what constitutes extremality of higher spin black holes. It has previously been proposed
that extremal black holes can be de ned in terms of the Jordan class of the holonomy around
a non-contractable cycle. Extending the above studies, we then classify solutions of sl(4j3)
sl(4j3) Chern-Simons theory in terms of extremality and supersymmetry, and nd non-extremal
supersymmetric black hole solutions. One of the results, in this higher-spin context, indicates
that supersymmetry and extremality do not imply each other. Finally, a review is made of hs[ ]
theory, which is constructed using Vasiliev theory. This is another useful tool in describing
higher spin theories, with the aim of extending hs[ ] to shs[ ], the supersymmetric analogue of
which might have its own extremal conditions.
