Abstract
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 ℓ, 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 \( {v}_B\left(T\gg \frac{1}{\ell}\right)=\sqrt{\frac{d}{2\left(d-1\right)}} \).
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Ahn, Y., Jahnke, V., Jeong, HS. et al. Scrambling in hyperbolic black holes: shock waves and pole-skipping. J. High Energ. Phys. 2019, 257 (2019). https://doi.org/10.1007/JHEP10(2019)257
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DOI: https://doi.org/10.1007/JHEP10(2019)257