For the case when the collision takes place on the horizon of the black hole ( r → r$_{H}$ ) the system (37)–(40) can be solved exactly In general case the system of three Eqs. (37)–(40) for four variables ε$_{1}$$_{µ}$, ε$_{2}$$_{µ}$, L$_{1}$$_{µ}$ , L$_{2}$$_{µ}$ can be solved numeri- cally for a fixed value of one variable (and fixed parameters m /µ, L$_{1}$ / M , L$_{2}$ / M , a / M , r / M ). The example of numerical solution is µ/ m = 0 . 3 , l$_{1}$ = 2 . 2 , l$_{2}$ = 2 . 198 , A = 0 . 99 , x = 1 . 21 , l$_{1}$$_{µ}$ = 16 . 35 , l$_{2}$$_{µ}$ = − 1 . 69 , ε$_{1}$$_{µ}$ = 7 . 215 , ε$_{2}$$_{µ}$ = − 0 . 548. Note that the energy of the second final particle is negative a nd the energy of the first final particle contrary to the limit obt ained in [11] is larger than the energy of initial particles as it must be in the case of a Penrose process [8]. If the mass of the parti- cle is not very large this particle is observed as ultrarelativistic. What is the reason of this contradiction? Let us investigate the problem carefully. Note that if one neglects the states with negative energy in ergosphere energy extracted in the considered process can not be larger than the initial energy of the pair of particles at infinity, i.e. 2 m . The same limit 2 m for the extracted energy for any (including Penrose process) scattering process in the vicinity of the black hole was obtained in [11]. Let us show why this conclusion is incorrect. If the angular momentum of the falling particles is the same then (see (40)) one has the situation similar to the usual decay of the particle with mass 2 m in two particles with mass µ . Due to the Penrose process in ergosphere it is possible that the particle falling inside the black hole has the negative relative to infinity energy and then the extracted particle can have energy larger than 2 m . The main assumption made in [11] is the supposition of the collinearity of vectors of 4-momenta of the particles falling in- side and outside of the black hole (see (9)–(11) in [11]). The authors of [11] say that these vectors are “asymptotically t an- gent to the horizon generator”. First note that from (8), (16) for A < 1 and l ≤ l$_{R}$ or A = 1, but l < 2 the limit of dr / d τ is not zero at the horizon. This derivative has opposite signs for the falling and outgoing parti- cles. Signs for other components of the 4-momentum are equal. In the limiting case ( A = 1, l$_{1}$ = 2) the expressions dt / d τ , d ϕ/ d τ of the components of the 4-velocity of the infalling par- ticle (6), (7) go to infinity when r → r$_{H}$ , but dr / d τ goes to zero. In spite of smallness of r -components in the expression of the square of the 4-momentum vector they have the factor g$_{rr}$ going to infinity at the horizon. So putting them to zero can lead to a mistake. To see if u$_{(1)}$ and v$_{(1)}$ are collinear it is necessary to put the coordinate r of the collision point to the limit r$_{H}$ = M and resolve the uncertainties ∞ $^{/}$∞ and 0 / 0. For the falling particle ε = 1, l = 2 the expressions for components of the 4-vector u can be easily found from (6)–(8). For the particle outgoing f rom the black hole due to exact solution on the horizon (43) one puts ε$_{1}$$_{µ}$ = l$_{1}$$_{µ}$ / 2 + α , where α is some function of r and l$_{1}$$_{µ}$ , such that α → 0 when r → r$_{H}$ . Putting this ε$_{1}$$_{µ}$ into (6)–(8) one gets for The authors are indebted to Ted Jacobson and Thomas P. Sotiriou for putting their attention to a numerical mistake in the first version of the paper [19]. In the vicinity of rotating black holes X$_{L}$ can decay on or- dinary particles as it is possible for the GU energies as well as they can be converted into X$_{S}$ decaying particles because 〈 $^{X$_{L}$}$|$^{X$_{S}$}$〉 GLYPH<nequal> 0. These decays can go with baryon and CP - conservation breaking, so that di ff erent hypotheses on the pro- cesses in the early Universe can be checked by astrophysical observations of AGN. All this confirms our hypothesis in [1] that the vicinity of th e rotating black hole is the arena of the Grand Unification phys ics as it was in the early Universe. In the early Universe gravitation created pairs of superheavy X , ˜ X particles decaying then as short living and long living X$_{S}$ , X$_{L}$ particles on ordinary quarks and leptons. But then due to the breaking of the GU symmetry X$_{L}$ became metastable and survived up to our time as dark matter particles. Due to the condition dt / d τ > 0 (movement forward in time) the necessary condition for collinearity is that both (44) and (45) must be zero, which is not true. This leads to the conclusion that the considerations of the authors of [11] for scattering exactly on the horizon can not be used for the real situation of particle scattering close to the horizon. x = r / M → 1 ε$_{1}$$_{µ}$ = AL$_{1}$$_{µ}$ 2 r$_{H}$ , ε$_{2}$$_{µ}$ = 2 m µ − AL$_{1}$$_{µ}$ 2 r$_{H}$ , L$_{2}$$_{µ}$ = m µ ( L$_{1}$ + L$_{2}$ ) − L$_{1}$$_{µ}$ . (43) v t (1) u t (1) = v ϕ (1) u ϕ (1) = α $^{x}$− 1 + l$_{1}$$_{µ}$ 2 , (44) v r (1) u r (1) $^{=}$− √ 2 α 2 ( $^{x}$− 1) 2 + 2 l$_{1}$$_{µ}$ α $^{x}$− 1 + 3 8 l 2 1 µ − 1 2 . (45) Acknowledgments References [1] A.A. Grib, Yu.V. Pavlov, Mod. Phys. Lett. A 23 (2008) 1151–1159. [2] The Pierre Auger Collaboration, Science 318 (2007) 938– 943; The Pierre Auger Collaboration, Astropart. Phys. 34 ( 2010) 314–326. [3] A.A. Grib, Yu.V. Pavlov, Int. J. Mod. Phys. D 11 (2002) 433–436; A.A. Grib, Yu.V. Pavlov, Int. J. Mod. Phys. A 17 (2002) 4435–4 439. [4] A.A. Grib, Yu.V. Pavlov, Grav. Cosmol. 15 (2009) 44–48. [5] R. 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