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Rotating Black Holes in AdS, Extremality and Chaos

Avik Banerjee, Arnab Kundu, Rohan R. Poojary

TL;DR

This work investigates extremal chaos in rotating AdS black holes by combining (i) near-horizon JT gravity analysis to capture thermal modes and their Schwarzian-driven OTOC growth, and (ii) probe-string worldsheet dynamics to access chaos in the dual CFT. It finds that, at extremality, chaos splits into two channels: thermal modes yielding λL = 2π T_H away from extremality and vanishing at extremality, and extremal (left-moving) AdS3 PBH modes yielding λL = 2r_+ that persist at extremality; in higher dimensions, the extremal chaos becomes a nontrivial function of the Frolov-Thorne temperatures. The results connect BTZ boundary analysis with throat dynamics, and extend the Kerr/CFT perspective to extremal chaos in AdS4, supported by worldsheet temperature calculations that reveal a consistent left-moving sector controlling the growth. Overall, the paper provides a two-pronged framework to understand scrambling at extremality and outlines the interplay between thermal and extremal modes as a route to extremal chaos in holographic CFTs.

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.

Rotating Black Holes in AdS, Extremality and Chaos

TL;DR

This work investigates extremal chaos in rotating AdS black holes by combining (i) near-horizon JT gravity analysis to capture thermal modes and their Schwarzian-driven OTOC growth, and (ii) probe-string worldsheet dynamics to access chaos in the dual CFT. It finds that, at extremality, chaos splits into two channels: thermal modes yielding λL = 2π T_H away from extremality and vanishing at extremality, and extremal (left-moving) AdS3 PBH modes yielding λL = 2r_+ that persist at extremality; in higher dimensions, the extremal chaos becomes a nontrivial function of the Frolov-Thorne temperatures. The results connect BTZ boundary analysis with throat dynamics, and extend the Kerr/CFT perspective to extremal chaos in AdS4, supported by worldsheet temperature calculations that reveal a consistent left-moving sector controlling the growth. Overall, the paper provides a two-pronged framework to understand scrambling at extremality and outlines the interplay between thermal and extremal modes as a route to extremal chaos in holographic CFTs.

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.

Paper Structure

This paper contains 15 sections, 112 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Chaos in BTZ
  3. JT analysis for near extremal BTZ
  4. Thermodynamics of JT model
  5. Thermal modes
  6. Extremal throat description
  7. Relating boundary and near horizon coordinates
  8. Probes in BTZ
  9. Extremal Kerr-$AdS_4$
  10. Thermal modes & near extremal chaos
  11. Extremal chaos
  12. Probing the Geometry
  13. Conclusion & Discussion
  14. Acknowledgements
  15. Robert's Transformations

Figures (1)

  • Figure 1: We have plotted the worldsheet temperature, in units of the Frolov-Thorne temperature $T_{FT}$, defined in eqn (\ref{['Kerr_ext_temp']}). Here curves corresponds to setting $r_0 = 1/2, 2/5, 1/3$, from top to bottom, respectively. Clearly, the curves end at $|\omega|=1$, which is the causality bound.