In [1] we put the hypothesis that Active Galactic Nuclei (AGN) can be the sources of ultrahigh energy particles in cos- mic rays observed recently by the AUGER group (see [2]) due to the processes of converting dark matter formed by super- heavy neutral particles into visible particles — quarks, leptons (neutrinos), photons. Such processes as it was discussed pre- viously in [3, 4] could lead to the origination of visible matter from the dark matter particles in the early Universe when the energy of particles was of the Grand Unification (GU) order (10 13 − 10$^{14}$GeV) i.e. at the end of inflation era. If AGN are rotating black holes then in [1] we discussed the idea that “This black hole acts as a cosmic supercollider in which superheavy particles of dark matter are accelerated close to the horizon to the GU energies and can be scattering in collisions.” It was also shown that in Penrose process [5] da rk matter particle can decay on two particles, one with the nega- tive energy, the other with the positive one and particles of very high energy of the GU order can escape the black hole. Then these particles due to interaction with photons close to the black hole will loose energy analogously up to the Greisen-Zatsepin- Kuzmin limit in cosmology [6]. Processes of converting dark matter particles into visible ones as well as collisions of dark matter particles close to the horizon of the black hole in the AGN can play important role in the solution of the problem of cusps as it was discussed in [7]. According to the hierarchical model the galaxies were formed due to initial inhomogeneities of dark matter distribution. But after origination of rotating black holes at the centre of future galaxies large part of the dark matter became redistributed so that it can be mainly present in the halo of galaxy [7]. In this paper we show that the energy of scattering in the cen- tre of mass system can be still unlimited in the cases of multiple scattering. In Section 2, we calculate this energy, reproduce the results of [9]–[11] and show that in some cases (multiple sca t- tering) the results of [10, 11] on the limitations of the scattering energy for nonextremal black holes are not valid. In Section 2.1 an evaluation of the time necessary for the freely falling parti- cle to get the unbounded large energy in collision with the other particle in the centre of mass system is made. It is proved that in order to have infinitely large energy of collision on the ho ri- zon infinitely large time from the beginning of free falling o f the particle on the rotating black hole is needed. Particle colli- sions inside the rotating black hole are considered in Section 3. In Section 4, we obtain the results for the extraction of the en- ergy after collision in the field of the Kerr’s metric. It occu rs First calculations of the scattering of particles in the ergo- sphere of the rotating black hole, taking into account the Pen- rose process, with the result that particles with high energy can escape the black hole, were made in [8]. Recently in [9] it was shown that for the rotating black hole (if it is close to the critical one) the energy of scattering is unlimited. The result of [9] was criticized in [10, 11] where the authors claimed that if the black hole is not a critical rotating black hole so that its dimension- less angular momentum A GLYPH<nequal> 1 but A = 0 . 998 then the energy is limited. The problem of the origin of ultrahigh energy cosmic rays (UHECR) is a major unsolved issue in astroparticle physics. Surely there can be di ff erent mechanisms of getting UHECR from AGN. Our aim is full investigation of the role of pro- cesses of collisions and decays of elementary particles close to the horizon of the Kerr black holes in the AGN. These parti- cles can be superheavy particles of dark matter or usual protons, iron nuclei, etc. In the latter cases for usual particles to get large energy one must consider multiple scattering. Scattering of particles in the gravitational field of Kerr bl ack holes is considered. It is shown that scattering energy of particles in the centre of mass system can obtain very large values not only for extremal black holes but also for nonextremal ones existing in Nature. This can be used for explanation of still unresolved problem of the origin of ultrahigh energy cosmic rays observed in Auger experiment. Extraction of energy after the collision is investigated. It is shown that due to the Penrose process the energy of the particle escaping the hole at infinity can be large. Contr adictions in the problem of getting high energetic particles escaping the black hole are resolved. Keywords: Black holes, Particle collisions, Cosmic rays arXiv:1001.0756v2 [gr-qc] 30 Jan 2011 1. Introduction Abstract On particle collisions in the gravitational field of the Kerr black hole A.A. Grib$^{a,b}$, Yu.V. Pavlov a,c $^{a}$A. Friedmann Laboratory for Theoretical Physics, 30 / 32 Griboedov can., St. Petersburg 191023, Russia $^{b}$Theoretical Physics and Astronomy Department, The Herzen University, 48, Moika, St. Petersburg 191186, Russia $^{c}$Institute of Mechanical Engineering, Russian Academy of Sciences, 61 Bolshoy, V.O., St. Petersburg 199178, Russia E-mail addresses: andrei_grib@mail.ru (A.A. Grib), yuri.pavlov@mail.ru (Yu.V. Pavlov)