content_image/413454.jpg content_image/413453.jpg content_image/413455.jpg content_image/413457.jpg content_image/413452.jpg content_image/413451.jpg content_image/413450.jpg
for l = l$_{R}$ and l = l$_{L}$ correspondingly. 

The dependence of the energy of collision E$_{c}$$_{.}$$_{m}$$_{.}$ on the radial coordinate for l$_{1}$ = l$_{R}$ , l$_{2}$ = l$_{L}$ (see (16)) is given on Fig. 1. The boldface line corresponds to A = 0 . 998, the ordinary curve 

<img src='content_image/413454.jpg'>

to A = 0 . 9, the dotted to A = 0 . 5, the line formed by points describes nonrotating black hole ( A = 0). The fractures on dense line, denoted by dotted lines correspond to values x = x$_{R}$ ( A ) M / r$_{H}$ ( A ) (see x$_{R}$ in (17)) i.e. to zeroes of the expressions in roots in formula (11). 

Putting the limiting values of angular momenta l$_{L}$ , l$_{R}$ into the formula (13) one obtains the maximal values of the energy of collision for particles falling from infinity 

<img src='content_image/413453.jpg'>

The dependence of c . m . hole is shown on Fig. 2. 

<img src='content_image/413455.jpg'>

For nonrotating black hole the maximal energy of collision due to (18) is E max c . m . / m = $_{2}$√$_{5 (first found in [12]).}$ 

For A = 1 − ϵ with ϵ → 0 formula (18) gives: m 

<img src='content_image/413457.jpg'>

(see (8) in [11]). So even for values close to the extremal A = 1 of the rotating black hole E max c . m . / m can be not very large as it is mentioned in [10, 11]. So for A$_{max}$ = 0 . 998 considered as the maximal possible dimensionless angular momentum of the astrophysical black holes (see [14]), from (18) one obtains E max c . m . / m ≈ 18 . 97. Does it mean that in real processes of particle scattering in the 

vicinity of the rotating nonextremal black holes the scattering energy is limited so that no Grand Unification or even Planck- ean energies can be obtained? Let us show that the answer is no! If one takes into account the possibility of multiple scat- tering so that the particle falling from the infinity on the bl ack hole with some fixed angular momentum changes its momen- tum in the result of interaction with particles in the accreting disc and after this is again scattering close to the horizon then the scattering energy can be unlimited. 

The limiting value of the angular momentum of the particle close to the horizon of the black hole can be obtained from the condition of positive derivative in (6) dt / d τ > 0, i.e. going “forward” in time. So close to the horizon one has the conditi on l < ε 2 x$_{H}$ / A which for ε = 1 gives the limiting value l$_{H}$ . 

From (8) one can obtain the permitted interval in r for parti- cles with ε = 1 and angular momentum l = $^{l$_{H}$}$− δ . In the second order in δ close to the horizon one obtains 

<img src='content_image/413452.jpg'>

If the particle falling from the infinity with l ≤ l$_{R}$ arrives to the region defined by (20) and here it interacts with other partic les of the accretion disc or it decays on more light particle so that it gets the larger angular momentum l$_{1}$ = l$_{H}$ − δ , then due to (13) the scattering energy in the centre of mass system is 

<img src='content_image/413451.jpg'>

and it increases without limit for δ → 0. For A$_{max}$ = 0 . 998 and l$_{2}$ = l$_{L}$ , E$_{c}$$_{.}$$_{m}$$_{.}$ ≈ 3 . 85 m / √$_{δ}$$_{.}$ Note that for rapidly rotating black holes A = 1 ϵ the dif- 

− ference between l$_{H}$ and l$_{R}$ is not large 

<img src='content_image/413450.jpg'>

For A$_{max}$ = 0 . 998, l$_{H}$ − l$_{R}$ ≈ 0 . 04 so the possibility of getting small additional angular momentum in interaction close to the horizon seems much probable. 

That is why we come to a conclusion that unboundedly large energy can be obtained in the centre of mass system of scatter- ing particles. This means that physical processes not only on the Grand Unification scale but even on the Planckean energy can go in this case. 

One can obtain the same result of getting unbounded large energy in the centre of mass frame for particles with di ff erent masses m$_{1}$ GLYPH<nequal> m$_{2}$ and ε$_{1}$ GLYPH<nequal> ε$_{2}$ [15]. 

However an important question is to look how particles with large energy can be extracted from the black hole? Some energy 

