Acceleration of particles by black holes as a result of deceleration: Ultimate manifestation of kinematic nature of BSW effect

The recently discovered so-called BSW effect consists in the unbound growth of the energy _Ec.m.$E_{\mathit{c}.\mathit{m}.}$ in the center of mass frame of two colliding particles near the black hole horizon. We consider a new type of the corresponding scenario when one of two particles (“critical”) remains at rest near the horizon of the charged near-extremal black hole due to balance between the attractive and repulsion forces. The other one hits it with a speed close to that of light. This scenario shows in a most pronounced way the kinematic nature of the BSW effect. In the extremal limit, one would gain formally infinite _Ec.m.$E_{\mathit{c}.\mathit{m}.}$ but this does not happen since it would have require the critical massive particle to remain at rest on the null horizon surface that is impossible. We also discuss the BSW effect in the metric of the extremal Reissner–Nordström black hole when the critical particle remains at rest near the horizon.