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

Tomohiro Harada, Hiroya Nemoto, and Umpei Miyamoto
Phys. Rev. D 86, 024027 – Published 17 July 2012; Erratum Phys. Rev. D 86, 069902 (2012)

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 fine-tuned, 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 134.3%. 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.

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  • Received 31 May 2012

DOI:https://doi.org/10.1103/PhysRevD.86.024027

© 2012 American Physical Society

Erratum

Authors & Affiliations

Tomohiro Harada1,2,*, Hiroya Nemoto1, and Umpei Miyamoto1

  • 1Department of Physics, Rikkyo University, Toshima, Tokyo 171-8501, Japan
  • 2Astronomy Unit, School of Physics and Astronomy, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom

  • *harada@rikkyo.ac.jp

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Issue

Vol. 86, Iss. 2 — 15 July 2012

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