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

Yongjun Ahn, Viktor Jahnke, Hyun-Sik Jeong, Keun-Young Kim
2019 Journal of High Energy 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 ). 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
more » ... rent 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 2π ) = 1 d−1 and the planar result v B (T 1 ) = d 2(d−1) .
doi:10.1007/jhep10(2019)257 fatcat:7f4hd5geuzcqnfx3n3ahcrxd3q