Fast Scrambling due to Rotating Shockwaves in BTZ

Abstract

We study the perturbation due to rotating shockwaves in BTZ geometries at late times and analyse the change in Mutual Information between the two subsystems belonging to the dual CFT L and CFT R . We find that the scrambling of Mutual Information is in general governed by the Lyapunov index λ L which is bounded by 2π β(1−µL) ≥ 2π β where µ = r − /r + and L is the angular momentum of the shockwave. For the special case of L=1 we find the Mutual Information analytically, characterized by λ L = κ/2 and with the scrambling time for large black holes t * = β(1−µ) π log S.

Scrambling time for analogue black holes embedded in AdS space

“…Therefore, as an attempt and exploration, we hope to consider whether there are similar possible effects in table-top acoustic black holes, and whether it can be falsified experimentally, so as to provide some hints for subsequent theoretical and experimental studies. At the last, our toy model is similar to the rotating BTZ in metric factor (in formula (1.6)), and we recently find some studies about shock waves in the rotating BTZ in [34]. Our main result (3.9) is similar with the result formula (4.17) in this paper (t * = β(1−µ) π log S βE ef f ).…”