Collision of spinning particles near BTZ black holes

We study the collision property of spinning particles near a Banados-Teitelboim-Zanelli (BTZ) black hole. Our results show that although the center-of-mass energy of two ingoing particles diverges if one of the particles possesses a critical angular momentum, however, particle with critical angular momentum can not exist outside of the horizon due to the violation of timelike constraint. Further detailed investigation indicates that only a particle with a subcritical angular momentum is allowed to exist near an extremal rotating BTZ black hole and the corresponding collision center-of-mass energy can be arbitrarily large in a critical angular momentum limit.