Particle Collisions in the Lower Dimensional Rotating Black Hole Space-Time with the Cosmological Constant

We study the effect of ultrahigh energy collisions of two particles with different energies near the horizon of a 2 + 1 dimensional BTZ black hole (BSW effect). We find that the particle with the critical angular momentum could exist inside the outer horizon of the BTZ black hole regardless of the particle energy. Therefore, for the nonextremal BTZ black hole, the BSW process is possible on the inner horizon with the fine tuning of parameters which are characterized by the motion of particle, while, for the extremal BTZ black hole, the particle with the critical angular momentum could only exist on the degenerated horizon, and the BSW process could also happen there.