Collisions of spinning massive particles in a Schwarzschild background

Abstract

It is known that the center-of-mass energy of the collision of two massive particles following geodesics around a black hole presents a maximum. The maximum energy increases when the black hole is endowed with spin, and for a maximally rotating hole this energy blows up, offering, in principle, a unique probe of fundamental physics. This work extends the latter studies by considering that the colliding particles possess intrinsic angular momentum (spin), described by the Hanson-Regge-Hojman theory of spinning particles. By analyzing planar trajectories of spinning particles around non-rotating black holes, a significant increase of the invariant collision energy is found. Radial turning points, causality constraints, and limitations of the theory are discussed.

Charged spinning black holes as accelerators of spinning particles

“…The CM energy for the extremal KN black hole near the horizon is (25) where the K 4 is defined in appendix A. We can see that when a 2 −j 1 a + 1 = 0 or a 2 −j 2 a + 1 = 0 the CM energy will be divergent and the critical total angular momentumj i = 1+a 2 a (i = 1, 2), which is the same as that of Ref.…”

“…The case with a = Q = 0 describes the Schwarzschild black hole as an accelerator of spinning test particles given in Ref. [25].…”

“…Note that the velocity vector u µ and the canonical momentum vector P µ of the spinning test particle are not parallel [22,25,[28][29][30], and the canonical momentum P µ satisfies P µ P µ = −m 2 which indicates that the canonical momentum vector keeps timelike along the trajectory. However, the velocity vector u µ of the spinning test particle might transform to be spacelike from timelike [22,25,28].…”

“…However, the velocity vector u µ of the spinning test particle might transform to be spacelike from timelike [22,25,28]. This can be avoided if one considers the reaction of the spinning test particles to the spacetime, and the results will be more accurate.…”

“…In Refs. [22,25,[28][29][30] show that the velocity vector u µ and the canonical momentum vector P µ of the spinning test particle are not parallel, and the velocity vector u µ might transform to be spacelike from timelike along the trajectory. So it is important to clarify the relation between the divergent region and the superluminal region in spin-angular space.…”