Special case of the Bañados-Silk-West effect

Abstract: If two particles collide near the rotating extremal black hole and one of them is fine-tuned, the energy in the center of mass frame $E_{c.m.}$ can grow unbounded. This is the so-called Ba~{n}ados-Silk-West (BSW) effect. Recently, another type of high energy collisions was considered in which all processes happen in the Schwarzschild background with free falling particles. If the Killing energy $E$ of one of particle is sufficiently small, $E_{c.m.}$ grows unbounded. We show that, however, such a particle cannot be created in any precedent collision with finite energies, angular momenta and masses. Therefore, in contrast to the standard BSW effect, this one cannot be realized if initial particles fall from infinity. If the black hole is electrically charged, such a type of collisions is indeed possible, when a particle with very small $E$ collides with one more particle coming from infinity. Thus the BSW effect is achieved due to collisions of neutral particles in the background of a charged black hole. This requires, however, at least two-step process.