Special case of the Ba\~{n}ados-Silk-West effect

TL;DR

This paper investigates a special case of the Ba extasciitilde{n}ados-Silk-West effect, showing that certain high-energy collisions near black holes require specific conditions and are not possible from infinity unless involving charged black holes and multi-step processes.

Contribution

It demonstrates that unbounded center-of-mass energy collisions with small Killing energy particles cannot originate from infinity in neutral black holes, but are possible with charged black holes through multi-step processes.

Findings

Unbounded $E_{c.m.}$ cannot originate from initial collisions with finite energies near neutral black holes.

High-energy collisions involving small $E$ particles are possible near charged black holes with multi-step processes.

The standard BSW effect requires fine-tuned particles near extremal rotating black holes, but the alternative process involves charged black holes.

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.