Rotating Black Holes in AdS, Extremality and Chaos

TL;DR

This paper explores how extremal rotating AdS black holes can exhibit maximal chaos in dual CFT correlators, revealing new insights into black hole thermodynamics and quantum chaos at extremality.

Contribution

It introduces a dual approach combining geometric mode analysis and probe string dynamics to study chaos in extremal rotating AdS black holes.

Findings

Extremal BTZ black holes show chaos governed by left-moving temperature.

Higher-dimensional AdS-Kerr black holes have chaos characterized by Frolov-Thorne temperatures.

Correlators in dual CFTs exhibit exponential growth at extremality.

Abstract

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.