Ultrahigh energy head-on collisions without horizons or naked singularities: General approach

Recently, alternatives to the Banados, Silk, and West effect were proposed which are (i) due to the existence of naked singularities instead of the horizon and (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 the unbound energy E-c.m. in the center-of-mass frame due to head-on collisions of particles near the would-be horizon. The energy measured at infinity can also be unbound. If self-gravitating shells collide, instead of particles, the underlying reason leading to unbound E-c.m. is the same.