On Particle Collisions in the Vicinity of Charged Black Holes

The process of particle collision in the vicinity of black holes is known to generate unbounded energies in the center-of-mass frame (the Bañados–Silk–West (BSW) effect) under specific conditions. We consider this process in the charged black hole metrics, namely, the Reissner–Nordström (RN) and Majumdar–Papapetrou (MP) metrics. We consider energy extraction from a Bardeen regular black hole due to the BSW effect. As in the RN case, we show that there is no restriction on energy extraction, but for real charged particles this effect is negligible. We derive necessary and sufficient conditions for this process. The conditions for the BSW effect in RN and MP metrics are shown to be identical, which is explained by the asymptotic equivalence of the two metrics near the horizons. Energy extraction in the RN metric is discussed. It is shown that if two real particles collide while falling onto a black hole, they are extremely unlikely to generate an ultra-massive particle. For the case of head-on collisions, we derive an upper bound on the extracted mass, which depends on the lapse function of the metric at the point of collision.