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 $\lambda_L$ 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 $t_*=\frac{\beta(1-\mu)}{\pi}\log S$.