Acceleration of particles by acceleration horizons

TL;DR

This paper investigates how particles can gain infinite energy during collisions near acceleration horizons, revealing a paradox and providing a new perspective on the Bañados-Silk-West effect from the viewpoint of horizon-crossing observers.

Contribution

It demonstrates the manifestation of the BSW effect near acceleration horizons and resolves the paradox related to coordinate dependence of the collision energy.

Findings

E_{c.m.} can become indefinitely large with fine-tuned parameters

A coordinate transformation can remove the horizon from the metric

Energy divergence depends on the observer's frame of reference

Abstract

We consider collision of two particles in the vicinity of the extremal acceleration horizon (charged or rotating) that includes the Bertotti-Robinson space-time and the geometry of the Kerr throat. It is shown that the energy in the centre of mass frame E_{c.m.} can become indefinitely large if parameters of one of the particles are fine-tuned, so the Ba\~nados-Silk-West (BSW) effect manifests itself. There exists coordinate transformation which brings the metric into the form free of the horizon. This leads to some paradox since (i) the BSW effect exists due to the horizon, (ii) E_{c.m.} is a scalar and cannot depend on the frame. Careful comparison of near-horizon trajectories in both frames enables us to resolve this paradox. Although globally the space-time structure of the metrics with acceleration horizons and black holes are completely different, locally the vicinity of the extremal black hole horizon can be approximated by the metric of the acceleration one. The energy of one particle from the viewpoint of the Kruskal observer (or the one obtained from it by finite local boost) diverges although in the stationary frame energies of both colliding particles are finite. This suggests a new explanation of the BSW effect for black holes given from the viewpoint of an observer who crosses the horizon. It is complementary to the previously found explanation from the point of view of a static or stationary observer.