Collisional Penrose process near the horizon of extreme Kerr black holes

TL;DR

This paper investigates the limits of energy extraction via the collisional Penrose process near extreme Kerr black holes, concluding that the maximum energy gain for escaping particles is modest despite high center of mass energies.

Contribution

It provides a detailed analysis showing that even in ideal conditions, energy extraction from black hole collisions is limited, challenging the idea of black holes as cosmic particle accelerators.

Findings

Maximum escaping particle energy is only modestly above initial energy.

High center of mass energy does not translate to high escape energy.

Collisional Penrose process has limited efficiency in energy extraction.

Abstract

Collisions of particles in black holes' ergospheres may result in an arbitrarily large center of mass energy. This led recently to the suggestion (Banados et al., 2009) that black holes can act as ultimate particle accelerators. If the energy of an outgoing particle is larger than the total energy of the infalling particles the energy excess must come from the rotational energy of the black hole and hence this must involve a Penrose process. However, while the center of mass energy diverges the position of the collision makes it impossible for energetic particles to escape to infinity. Following an earlier work on collisional Penrose processes (Piran & Shaham 1977) we show that even under the most favorable idealized conditions the maximal energy of an escaping particle is only a modest factor above the total initial energy of the colliding particles. This implies that one shouldn't expect collisions around a black hole to act as spectacular cosmic accelerators.