Special case of the Ba~{n}ados-Silk-West effect. (arXiv:2006.11552v3 [gr-qc] UPDATED)

Special case of the Ba~{n}ados-Silk-West effect. (arXiv:2006.11552v3 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Zaslavskii_O/0/1/0/all/0/1">O. B. Zaslavskii</a>

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.

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.

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