High energy physics in the vicinity of rotating black holes

The aim of the paper is the consideration of particle collisions in the vicinity of the horizon of rotating black holes. Existence of geodesics for massive and massless particles arising from the region inside of the gravitational radius in ergosphere leads to the different possibilities to get very high energy in the centre mass frame of two particles. The classification of all such geodesics on the basis of the proved theorem for extremal spherical orbits is given. Case of the unlimited growth of energy for the situation when one of the particles (the critical one) is moving along the "white hole" geodesic with the close to the upper limit angular momentum while the other particle is on the usual geodesic and the case of the unlimited negative angular momentum of the first particle are considered.