Rotating black holes in AdS spacetime, extremality, and chaos

Abstract

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.