Ultra-high-energy head-on collisions without horizons or naked singulrities: general approach

Abstract: Recently, alternatives to the Ba~nados, Silk and West (BSW) effect were proposed which are (i) due to the existence of naked singularities instead of the horizon, (ii) require neither horizon nor naked singularity. We reveal the main features of such alternatives in a model-independent way. The metric should be close to that of the extremal black hole but the horizon should not form. Then, one can gain unbound the energy E_{c.m.} in the centre of mass frame due to head-on collision of particles near the would-be horizon. The energy measured at infinity can also be unbound. If instead of particles self-gravitating shells collide, the underlying reason leading to unbound E_{c.m.} is the same.