Rotating black holes in AdS spacetime, extremality, and chaos

Extremal black holes have vanishing Hawking temperatures. In this paper, we argue that for asymptotically anti–de Sitter (AdS) black holes, at extremality, a particular class of correlators in the dual conformal field theory can exhibit exponential, maximally chaotic growth with a nonvanishing temperature. Our approach, at extremality, is twofold. First, we geometrically investigate the modes that are responsible for chaos. Second, we study the dynamics of a probe string to capture chaos in world sheet correlators. For rotating Banados-Teitelboim-Zanelli at extremality, the corresponding Lyapunov exponent is determined by the left-moving temperature. In higher dimensional AdS-Kerr geometries, on the other hand, the corresponding Lyapunov exponent becomes a nontrivial function of the Frolov-Thorne temperatures.