Fast scrambling due to rotating shockwaves in BTZ

We study the perturbation due to rotating shockwaves in Banados-Teitelboim-Zanelli geometries at late times and analyze change mutual information between two subsystems belonging dual ${\mathrm{CFT}}_{L}$ ${\mathrm{CFT}}_{R}$. find that scrambling of is general governed by Lyapunov index ${\ensuremath{\lambda}}_{L}$ which bounded $\ensuremath{\kappa}=\frac{2\ensuremath{\pi}}{\ensuremath{\beta}(1\ensuremath{-}\ensuremath{\mu}\mathcal{L})}\ensuremath{\ge}\frac{2\ensuremath{\pi}}{\ensuremath{\beta}}$, where $\ensuremath{\mu}={r}_{\ensuremath{-}}/{r}_{+}$ $\mathcal{L}$ angular momentum shockwave. For special case $\mathcal{L}=1$ we analytically show it characterized ${\ensuremath{\lambda}}_{L}=\ensuremath{\kappa}/2$ with time for large black holes given as ${t}_{*}=\frac{\ensuremath{\beta}(1\ensuremath{-}\ensuremath{\mu})}{\ensuremath{\pi}}\mathrm{log}S$.