The Ba\~nados-Silk-West effect with immovable particles near static black holes and its rotational counterpart

Abstract

The BSW effect implies that the energy $E_{c.m.}$ in the center of mass frame of two particles colliding near a black hole can become unbounded. Usually, it is assumed that particles move along geodesics or electrogeodesics. Instead, we consider another version of this effect. One particle is situated at rest near a static, generally speaking, distorted black hole. If another particle (say, coming from infinity) collides with it, the energy of collision $E_{c.m.}$ in the center of mass frame grows unbounded (the BSW effect). The force required to keep such a particle near a black hole diverges for nonextremal horizons but remains finite nonzero for extremal one and vanishes in the horizon limit for ultraextremal black holes. Generalization to the rotating case implies that a particle corotates with a black hole but does not have a radial velocity. In doing so, the energy $E\rightarrow 0$, provided the angular momentum $L=0$. This condition replaces that of fine-tuning parameters in the standard version of the BSW effect.