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 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 λ_L which is bounded by κ =2/π β (1 -μ L ) ≥2/π β , where μ =r_-/r₊ and L is the angular momentum of the shockwave. For the special case of L =1 we find the mutual information analytically and show that it is characterized by λ_L=κ /2 with the scrambling time for large black holes given as t_*=β/(1 -μ ) π log S .