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

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 finetuned, 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. The present paper places the baseline for the study of particle emission from high-energy collision near a rapidly rotating black hole.

The Distribution and Annihilation of Dark Matter Around Black Holes

“…It has been noted repeatedly in recent works that the net energy gained through the Penrose process is quite modest, as is the fraction of collision products that might escape, and thus the astrophysical importance of the BSW effect is questionable (Jacobson & Sotiriou 2010;Bañados et al 2011;Bejger et al 2012;Harada et al 2012;McWilliams 2013). We argue here that two primary factors (to our knowledge largely neglected in previous work) could greatly enhance the astrophysical relevance and observability of this annihilation.…”

“…Earlier analytic work predicted that the maximum energy attainable from the collisional Penrose process was m 2.6 c for particles falling from rest at infinity (Bejger et al 2012;Harada et al 2012). Because our calculation is fully numerical, it was able to reveal previously unknown trajectories leading to very Figure 11.…”

Bañados-Silk-West effect with nongeodesic particles: Extremal horizons

“…Correspondingly, the BSW-2 effect can be realized near such horizons. 10 Another, more detailed classification of trajectories and corresponding types of the BSW effect can be found in Sec. IV of [16] for the Kerr metric and in [21] for general dirty rotating axially symmetric black holes.…”

“…near the horizon and the properties of energies of the collision outcome measured at infinity. The typical energies at infinity are quite modest even in the absence of force [9][10][11], so taking the force into account can only change them slightly. It is the first aspect which is nontrivial and is being discussed in the present paper.…”

Center of mass energy of colliding electrically neutral particles and super-Penrose process

“…However, detailed investigations showed that rotating neutral black holes are not pertinent for this purpose in the BSW scenario, so in spite of unbounded E c.m. , the energy E gained in the BSW process, remains quite modest [5] - [7]. Another type of scenario in which a fine-tuned outgoing particle experiences head-on collision with an incoming one increases the efficiency of the process [8] but, anyway, it remains bounded [9] - [12].…”