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

TL;DR

This paper demonstrates that the maximum center-of-mass energy in the collisional Penrose process around a black hole is limited by horizon formation constraints, contradicting previous claims of unbounded energy growth.

Contribution

It introduces a new upper bound on the center-of-mass energy in black hole collisions based on Thorne's hoop conjecture, refining previous theoretical predictions.

Findings

The center-of-mass energy is bounded and cannot grow unboundedly.

A new horizon forms before particles reach the original black hole horizon.

The maximum energy scales as (M/μ)^{1/4}, where M is black hole mass and μ is particle mass.

Abstract

Following the interesting work of Ba\~nados, Silk, and West [Phys. Rev. Lett. {\bf 103}, 111102 (2009)], it is repeatedly stated in the physics literature that the center-of-mass energy, ${\cal E}_{\text{c.m}}$, 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 ${\cal E}^{\text{max}}_{\text{c.m}}/2\mu\propto(M/\mu)^{1/4}$, where $M$ and $\mu$ are respectively the mass of the central black hole and the proper mass of the colliding particles.