Kerr black holes as accelerators of spinning test particles

TL;DR

This paper investigates how spinning test particles near extremal Kerr black holes can achieve arbitrarily high collision energies, extending previous geodesic-based studies to include spin effects using the Mathisson-Papapetrou-Dixon equation.

Contribution

It demonstrates that spinning particles can reach infinite collision energies near extremal Kerr black holes, with a critical angular momentum condition similar to non-spinning cases.

Findings

High-energy collisions occur near extremal Kerr horizons for spinning particles.

Critical angular momentum condition remains unchanged despite spin effects.

Infinite energies are not possible near non-extremal Kerr black holes.

Abstract

It has been shown that ultraenergetic collisions can occur near the horizon of an extremal Kerr black hole. Previous studies mainly focused on geodesic motions of particles. In this paper, we consider spinning test particles whose orbits are non-geodesic. By employing the Mathisson-Papapetrou-Dixon equation, we find the critical angular momentum satisfies $J=2E$ for extremal Kerr black holes. Although the conserved angular momentum $J$ and energy $E$ have been redefined in the presence of spin, the critical condition remains the same form. If a particle with this angular momentum collides with another particle arbitrarily close to the horizon of the black hole, the center-of-mass energy can be arbitrarily high. We also prove that arbitrarily high energies cannot be obtained for spinning particles near the horizons of non-extremal Kerr black holes.