Rotating Black Holes in AdS, Extremality and Chaos

Extremal black holes have vanishing Hawking temperatures. In this article, we argue that for asymptotically AdS black holes, at extremality, a particular class of correlators in the dual CFT can exhibit exponential, maximally chaotic growth with a non-vanishing temperature. Our approach, at extremality, is two-fold. First, we geometrically investigate the modes that are responsible for chaos. Secondly, we study the dynamics of a probe string to capture chaos in worldsheet correlators. For rotating BTZ 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 non-trivial function of the Frolov-Thorne temperatures.