Upper bounds on collisional penrose processes near rotating black-hole horizons

In this paper, we develop a general formalism for calculating energies of particles which escape to infinity after a collision in black-hole ergospheres. A few examples, in particular the Compton scattering, are discussed. For the latter, some model numerical calculations are presented which demonstrate the conversion of infalling low-energy photons into soft rays by equatorial plasma rings in black-hole ergospheres. The main conclusion to be drawn from this paper is that Compton-Penrose processes in black-hole ergospheres could produce characteristic soft rays, whose spectrum is strongly governed by the electron mass, and rather weakly controlled by other parameters. Such Penrose processes seem to be quite unique to black holes, and further thought might be given to their possible realizations in astrophysics. The processes are only effective in rapidly rotating black holes.