High efficiency of collisional Penrose process requires heavy particle production

Understand

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 Ba$\rm \tilde n$ados-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 to be 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 $(2+\sqrt{3})^2 \simeq 13.9$.