Journal of High Energy Physics

, 2019:257 | Cite as

Scrambling in hyperbolic black holes: shock waves and pole-skipping

  • Yongjun Ahn
  • Viktor Jahnke
  • Hyun-Sik Jeong
  • Keun-Young KimEmail author
Open Access
Regular Article - Theoretical Physics


We study the scrambling properties of (d + 1)-dimensional hyperbolic black holes. Using the eikonal approximation, we calculate out-of-time-order correlators (OTOCs) for a Rindler-AdS geometry with AdS radius , which is dual to a d-dimensional conformal field theory (CFT) in hyperbolic space with temperature T = 1/(2π ℓ). We find agreement between our results for OTOCs and previously reported CFT calculations. For more generic hyperbolic black holes, we compute the butterfly velocity in two different ways, namely: from shock waves and from a pole-skipping analysis, finding perfect agreement between the two methods. The butterfly velocity vB (T) nicely interpolates between the Rindler-AdS result \( {v}_B\left(T=\frac{1}{2\pi \ell}\right)=\frac{1}{d-1} \) and the planar result \( {v}_B\left(T\gg \frac{1}{\ell}\right)=\sqrt{\frac{d}{2\left(d-1\right)}} \).


Gauge-gravity correspondence Holography and condensed matter physics (AdS/CMT) 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Yongjun Ahn
    • 1
  • Viktor Jahnke
    • 1
  • Hyun-Sik Jeong
    • 1
  • Keun-Young Kim
    • 1
    Email author
  1. 1.School of Physics and ChemistryGwangju Institute of Science and TechnologyGwangjuKorea

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