Ba\~{n}ados-Silk-West effect with nongeodesic particles: extremal horizons

TL;DR

This paper investigates whether the Ba extasciitilde{n}ados-Silk-West effect, which allows for arbitrarily high collision energies near black hole horizons, persists when particles are subject to non-gravitational forces, finding it generally survives under broad conditions.

Contribution

The study develops a model-independent framework to analyze the BSW effect with nongeodesic particles near extremal horizons, challenging previous beliefs about force restrictions.

Findings

The BSW effect persists under general conditions with finite radial force.

Azimuthal force must tend to zero sufficiently fast for the effect to remain large.

Even with restricted energy growth, collision energies remain very high for small forces.

Abstract

The Ba\~{n}ados-Silk-West (BSW) effect consists in the possibility to obtain arbitrarily large energy $E_{c.m.}$ in the centre of mass frame of two colliding particles near the black hole horizon. One of the common beliefs was that the action of force on these particles (say, due to gravitational radiation) should necessarily restrict the growth of $E_{c.m.}$. We consider extremal horizons and develop a model-independent approach and analyze the conditions for the force to preserve or kill the effect, using the frames attached both to observers orbiting the black hole and to ones crossing the horizon. We argue that the aforementioned expectations are not confirmed. Under rather general assumptions, the BSW effect survives. For equatorial motion it is only required that in the proper frame the radial component of the force be finite, while the azimuthal one tend to zero not too slowly. If the latter condition is violated, we evaluate $E_{c.m.}$, which becomes indeed restricted but remains very large for small forces.