Kerr naked singularities as particle accelerators

We investigate here the particle acceleration by Kerr naked singularities. We consider a collision between particles dropped in from infinity at rest, which follow geodesic motion in the equatorial plane, with their angular momenta in an appropriate finite range of values. When an event horizon is absent, an initially infalling particle turns back as an outgoing particle, when it has the angular momentum in an appropriate range of values, which then collides with infalling particles. When the collision takes place close to what would have been the event horizon in the extremal case, the center-of-mass energy of the collision is arbitrarily large, depending on how close the overspinning Kerr geometry is to the extremal case. Thus, the fast rotating Kerr configurations if they exist in nature could provide an excellent cosmic laboratory to probe ultrahigh-energy physics.