High energy physics in the vicinity of rotating black holes

We consider particle collisions in the vicinity of the horizon of rotating black holes. We show that the existence of geodesics for both massive and massless particles coming from inside the gravitational radius leads to different possibilities for an unboundedly high collision energy to appear in the center-of-mass frame of two particles. We give a classification of such geodesics in the general case based on a proved theorem for extremal spherical orbits. We analyze the case of the unbounded energy increase in the situation where one (critical) particle moves along the "white hole" geodesic with an angular momentum close to the bound while the other particle falls along an ordinary geodesic and the case of an unbounded negative angular momentum of the first particle.