Fast Scrambling due to Rotating Shockwaves in BTZ

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