Black-hole bomb, confined Penrose process and particle decay near singularity

We consider the decay of a particle with some energy E_0 > 0 inside the ergosphere of a black hole. After the first decay, one of the particles with the energy E_1 < 0 falls towards a black hole while the second one with E_2 > E_0 moves in the outward direction. It bounces back from a reflecting shell and, afterwards, the process repeats. For radial motion of charged particles in the Reissner-Nordstrom metric, the result depends
strongly on a concrete scenario. In particular, an indefinitely large growth of energy inside a shell is possible that gives rise to a black-hole bomb. We also consider a similar multiple process with neutral particles in the background of a rotating axially symmetric stationary black hole. We demonstrate that, if particle decay occurs at the turning point, a black-hole bomb in this case is impossible at all. For a generic point inside the ergoregion, there is a condition for a black-hole bomb to exist. It relates the ratio of masses before and after decay and the velocity of a fragment in the center of mass frame. One more process (decay near naked singularity) is also considered).