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Scrambling in Hyperbolic Black Holes: shock waves and pole-skipping · Around

2019

Scrambling in Hyperbolic Black Holes: shock waves and pole-skipping

Ahn, Yongjun, Jahnke, Viktor, Jeong, Hyun-Sik et al.

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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 $\ell$, which is dual to a $d-$dimensional conformal field theory (CFT) in hyperbolic space with temperature $T = 1/(2 \pi \ell)$.
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.

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