Upper bound on the center-of-mass energy of the collisional Penrose process

Abstract

Following the interesting work of Bañados, Silk, and West [Phys. Rev. Lett. {\bf 103}, 111102 (2009)], it is repeatedly stated in the physics literature that the center-of-mass energy, ${\mathcal{E}}_{\text{c.m}}$, of two colliding particles in a maximally rotating black-hole spacetime can grow unboundedly. For this extreme scenario to happen, the particles have to collide at the black-hole horizon. In this paper we show that Thorne's famous hoop conjecture precludes this extreme scenario from occurring in realistic black-hole spacetimes. In particular, it is shown that a new (and larger) horizon is formed {\it before} the infalling particles reach the horizon of the original black hole. As a consequence, the center-of-mass energy of the collisional Penrose process is {\it bounded} from above by the simple scaling relation ${\mathcal{E}}_{\text{c.m}}^{\text{max}}/2\mu \propto (M/\mu {)}^{1/4}$, where $M$ and $\mu$ are respectively the mass of the central black hole and the proper mass of the colliding particles.

5 pages

References in corpus (2)

• Collisional Penrose process near the horizon of extreme Kerr black holes
• Revised upper limit to energy extraction from a Kerr black hole

Cited by in corpus (5)

• The Collisional Penrose Process
• Kerr-Sen Black Hole as Accelerator for Spinning Particles
• Exploring black holes as particle accelerators: hoop-radius, target particles and escaping conditions
• Bañados-Silk-West effect with finite forces near different types of horizons: general classification of scenarios
• BSW phenomenon for near-fine-tuned particles with external force: general classification of scenarios