Universality of BSW mechanism for spinning particles

TL;DR

This paper investigates the BSW mechanism for spinning particles around rotating black holes, revealing conditions for infinite collision energy and demonstrating its limitations for nonextremal black holes, with universal applicability across gravity theories.

Contribution

It extends the BSW mechanism to spinning particles using a general rotating black hole metric and clarifies the conditions under which infinite energy collisions occur or are prevented.

Findings

High-energy collisions occur near-extremal black holes when energy-angular momentum relation is met.

The BSW mechanism fails for nonextremal black holes due to the breakdown of critical conditions.

Particles with critical spin cannot reach the horizon, preventing infinite energy collisions outside the horizon.

Abstract

Ba\~nados $et\, al.$ (BSW) found that Kerr black holes can act as particle accelerators with collisions at arbitrarily high center-of-mass energies. Recently, collisions of particles with spin around some rotating black holes have been discussed. In this paper, we study the BSW mechanism for spinning particles by using a metric ansatz which describes a general rotating black hole. We notice that there are two inequivalent definitions of center-of-mass (CM) energy for spinning particles. We mainly discuss the CM energy defined in terms of the worldline of the particle. We show that there exists an energy-angular momentum relation $e = \Omega_h j$ that causes collisions with arbitrarily high energy near-extremal black holes. We also provide a simple but rigorous proof that the BSW mechanism breaks down for nonextremal black holes. For the alternative definition of the CM energy, some authors find a new critical spin relation that also causes the divergence of the CM mass. However, by checking the timelike constraint, we show that particles with this critical spin cannot reach the horizon of the black hole. Further numerical calculation suggests that such particles cannot exist anywhere outside the horizon. Our results are universal, independent of the underlying theories of gravity.