  In this paper, we investigate the entanglement entropy of the rotating BTZ
black hole perturbed by a massive back-reacting free falling particle. Then,
mutual information between two finite intervals in two asymptotic regions of
rotating BTZ is derived. It allows us to find the scrambling time, the time
scale in which mutual information vanishes. We give a dual large $c$ CFT
description in terms of a thermofield double state with different temperatures
for left and right moving modes that is perturbed by a local operator. Exact
matching between gravity and CFT results is obtained.
