Fast Scrambling due to Rotating Shockwaves in BTZ

TL;DR

This paper investigates how rotating shockwaves in BTZ black holes influence the scrambling of information, revealing bounds on Lyapunov exponents and providing analytical results for mutual information decay.

Contribution

It introduces a detailed analysis of rotating shockwaves in BTZ geometries and derives bounds on Lyapunov indices affecting information scrambling.

Findings

Scrambling governed by Lyapunov index ; bounded by .

Analytical expression for mutual information at .

Scrambling time scales logarithmically with entropy for large black holes.

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 $\lambda_L$ which is bounded by $\kappa=\frac{2\pi}{\beta(1-\mu\mathcal{L})}\geq \frac{2\pi}{\beta}$ where $\mu=r_-/r_+$ and $\mathcal{L}$ is the angular momentum of the shockwave. For the special case of $\mathcal{L}$=$1$ we find the Mutual Information analytically and show that it is characterized by $\lambda_L=\kappa/2$ with the scrambling time for large black holes given as $t_*=\frac{\beta(1-\mu)}{\pi}\log S$.