Maximal efficiency of the collisional Penrose process

The c.m. energy in a collisional Penrose process - a collision taking place within the ergosphere of a Kerr black hole - can diverge under suitable extreme conditions (maximal Kerr, near horizon collision and suitable impact parameters). We present an analytic expression for the c.m. energy, refining expressions given in the literature. Even though the c.m. energy diverges, we show that the maximal energy attained by a particle that escapes the black hole's gravitational pull and reaches infinity is modest. We obtain an analytic expression for the energy of an escaping particle resulting from a collisional Penrose process, and apply it to derive the maximal energy and the maximal efficiency for several physical scenarios: pair annihilation, Compton scattering, and the elastic scattering of two massive particles. In all physically reasonable cases (in which the incident particles initially fall from infinity towards the black hole), the maximal energy (and the corresponding efficiency) are only 1 order of magnitude larger than the rest mass energy of the incident particles. The maximal efficiency found is ≈13.92 and it is obtained for the scattering of an outgoing massless particle by a massive particle.