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

Following the interesting work of Bañados, Silk, and West (2009) [6], it is repeatedly stated in the physics literature that the center-of-mass energy, Ec.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 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 bounded from above by the simple scaling relation Ec.mmax/2μ∝(M/μ)1/4, where M and μ are respectively the mass of the central black hole and the proper mass of the colliding particles.

Abstract licence: CC BY

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