Upper limits of particle emission from high-energy collision and reaction near a maximally rotating Kerr black hole

TL;DR

This paper analytically investigates the maximum energy and efficiency limits of particle emission from high-energy collisions near a maximally rotating Kerr black hole, demonstrating that energy extraction is possible but bounded.

Contribution

It provides the first analytical derivation of universal upper limits on emitted particle energy and extraction efficiency in such high-energy black hole collisions.

Findings

Maximum emitted particle energy is 218.6% of injected critical particle energy.

Maximum energy extraction efficiency is 146.6%.

Net positive energy can be extracted via elastic collision, Compton scattering, and pair annihilation.

Abstract

The center-of-mass energy of two particles colliding near the horizon of a maximally rotating black hole can be arbitrarily high if the angular momentum of either of the incident particles is fine-tuned, which we call a critical particle. We study particle emission from such high-energy collision and reaction in the equatorial plane fully analytically. We show that the unconditional upper limit of the energy of the emitted particle is given by 218.6% of that of the injected critical particle, irrespective of the details of the reaction and this upper limit can be realized for massless particle emission. The upper limit of the energy extraction efficiency for this emission as a collisional Penrose process is given by 146.6%, which can be realized in the collision of two massive particles with optimized mass ratio. Moreover, we analyze perfectly elastic collision, Compton scattering, and pair annihilation and show that net positive energy extraction is really possible for these three reactions. The Compton scattering is most efficient among them and the efficiency can reach 137.2%. On the other hand, our result is qualitatively consistent with the earlier claim that the mass and energy of the emitted particle are at most of order the total energy of the injected particles and hence we can observe neither super-heavy nor super-energetic particles.