Ultra-high energy collisions in static space-times: single versus multi-black hole cases

Abstract: We consider collision of two particles near static electrically charged extremal black holes and elucidate the conditions under which the energy in the centre of mass frame E_{c.m.} grows unbounded. For a single black hole, we generalize the results obtained earlier for the Reissner-Nordstr\"om metric, to distorted black holes. In the multi-black hole space-time, qualitatively new features appear. If the point of collision is close to at least two horizons simultaneously, unbounded E_{c.m.} are possible (i) without fine-tuning of particles' parameters, (ii) for an arbitrary mutual orientation of two velocities. Such a combination of properties (i) and (ii) has no analogues in the single black hole case and facilitates the condition of getting unbounded E_{c.m.}. Collisions in the electro-vacuum Majumdar-Papapetrou metric (several extremal black holes in equilibrium) is analyzed explicitly.