Schwarzschild black hole surrounded by quintessential matter field as an accelerator for spinning particles

TL;DR

This paper investigates how a Schwarzschild black hole surrounded by quintessential matter can act as a particle accelerator, with unbounded collision energies near the horizon when particles are near-critical and fine-tuned.

Contribution

It introduces the effect of quintessential matter on particle collisions near black holes and analyzes the conditions for unbounded energy growth with spinning particles.

Findings

Unbounded collision energy possible near the horizon for near-critical particles.

Energy divergence constrained by the Møller spin limit behind the horizon.

Conditions for subluminal motion and radial turning points are discussed.

Abstract

We study the collision of two massive particles with non-zero intrinsic spin moving in the equatorial plane in the background of a Schwarzschild black hole surrounded by quintessential matter field (SBHQ). For the quintessential matter equation of state (EOS) parameter, we assume three different values. It is shown that for collisions outside the event horizon, but very close to it, the centre-of-mass energy ($E_{\rm CM}$) can grow without bound if exactly one of the colliding particles is what we call near-critical, i.e., if its constants of motion are fine tuned such that the time component of its four-momentum becomes very small at the horizon. In all other cases, $E_{\rm CM}$ only diverges behind the horizon if we respect the M{\o}ller limit on the spin of the particles. We also discuss radial turning points and constraints resulting from the requirement of subluminal motion of the spinning particles.