On collisions with unlimited energies in the vicinity of Kerr and   Schwarzschild black hole horizons
  Two particle collisions close to the horizon of the rotating nonextremal Kerr's and Schwarzschild black holes are analyzed. For the case of multiple collisions it is shown that high energy in the centre of mass frame occurs due to a great relative velocity of two particles and a large Lorentz factor. The dependence of the relative velocity on the distance to horizon is analyzed, the time of movement from the point in the accretion disc to the point of scattering with large energy as well as the time of back movement to the Earth are calculated. It is shown that they have reasonable order. 
A. A. Grib, Yu. V. Pavlov and O. F. Piattella
gr-qc