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,the particle with critical angular momentum cannot exist outside of the horizon due to violation of the 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.