Acceleration of particles by rotating black holes: Near-horizon geometry and kinematics

Nowadays, the effect of unbound energy in the center-of-mass frame due to near-horizon collisions attracts much attention. We show the generality of the effect combining two seemingly completely different approaches based on the properties of a particle with respect to its local light cone and calculating its velocity in the locally non-rotating frame directly. In doing so, we do not assume that particles move along geodesics. Usually, a particle reaches a horizon having a velocity equal to that of light. However, there is also a case of "critical" particles for which this is not true. It is just a pair of usual and critical particles that leads to the effect under discussion. A similar analysis is carried out for massless particles. Then, critical particles are distinguishable due to finiteness of the local frequency. Thus both approach based on geometric and kinematic properties of particles moving near the horizon, reveal a universal nature of the effect.