Black holes and particles with zero or negative energy

We study properties of particles with zero or negative energy and a nonzero orbital angular momentum in the ergosphere of a rotating black hole. We show that the sign of the particle energy is uniquely determined by the angular velocity of its rotation in the ergosphere. We give a simple proof of the fact that extreme black holes cannot exist. We investigate the question of the possibility of an unlimited energy increase in the center-of-mass system of two colliding particles, one or both of which have negative or zero energy.