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Scrambling in hyperbolic black holes: shock waves and pole-skipping
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Journal Article
Scrambling in hyperbolic black holes: shock waves and pole-skipping
2019
Overview
A
bstract
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
/
(2
π 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
v
B
(
T
) nicely interpolates between the Rindler-AdS result
v
B
T
=
1
2
π
ℓ
=
1
d
−
1
and the planar result
v
B
T
≫
1
ℓ
=
d
2
d
−
1
.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V,SpringerOpen
