High efficiency of collisional Penrose process requires heavy particle production

The center-of-mass energy of two particles can become arbitrarily large if they collide near the event horizon of an extremal Kerr black hole, which is called the Banados-Silk-West (BSW) effect. We consider such a high-energy collision of two particles which started from infinity and follow geodesics in the equatorial plane and investigate the energy extraction from such a high- energy particle collision and the production of particles in the equatorial plane. We analytically show that, on the one hand, if the produced particles are as massive as the colliding particles, the energy-extraction efficiency is bounded by 2.19 approximately. On the other hand, if a very massive particle is produced as a result of the high-energy collision, which has negative energy and necessarily falls into the black hole, the upper limit of the energy-extraction efficiency is increased to (2+ √ 3) 2 ≃ 13.9. Thus, higher efficiency of the energy extraction, which is t ypically as large as