  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.
