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