Infinite efficiency of the collisional Penrose process: Can a overspinning Kerr geometry be the source of ultrahigh-energy cosmic rays and neutrinos?

Mandar Patil, Tomohiro Harada, Ken-ichi Nakao, Pankaj S. Joshi, and Masashi Kimura
Phys. Rev. D 93, 104015 – Published 9 May 2016

Abstract

The origin of the ultrahigh-energy particles we receive on Earth from outer space such as EeV cosmic rays and PeV neutrinos remains an enigma. All mechanisms known to us currently make use of electromagnetic interaction to accelerate charged particles. In this paper, we propose a mechanism exclusively based on gravity rather than electromagnetic interaction. We show that it is possible to generate ultrahigh-energy particles starting from particles with moderate energies using the collisional Penrose process in an overspinning Kerr spacetime transcending the Kerr bound only by an infinitesimal amount, i.e., with the Kerr parameter a=M(1+ε), where we take the limit ε0+. We consider two massive particles starting from rest at infinity that collide at r=M with divergent center-of-mass energy and produce two massless particles. We show that massless particles produced in the collision can escape to infinity with the ultrahigh energies exploiting the collisional Penrose process with the divergent efficiency η1/ε. Assuming the isotropic emission of massless particles in the center-of-mass frame of the colliding particles, we show that half of the particles created in the collisions escape to infinity with the divergent energies, while the proportion of particles that reach infinity with finite energy is minuscule. To a distant observer, ultrahigh-energy particles appear to originate from a bright spot which is at the angular location ξ2M/robs with respect to the singularity on the side which is rotating toward the observer. We compute the spectrum of the high-energy massless particles and show that anisotropy in the emission in the center-of-mass frame leaves a distinct signature on its shape. Since the anisotropy is dictated by the differential cross section of the underlying particle physics process, the observation of the spectrum can constrain the particle physics model and serve as a unique probe into fundamental physics at ultrahigh energies at which particles collide. Thus, the existence of the near-extremal overspinning Kerr geometry in the Universe, either as a transient or permanent configuration, would have deep implications on astrophysics as well as fundamental particle physics.

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  • Received 28 October 2015

DOI:https://doi.org/10.1103/PhysRevD.93.104015

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Mandar Patil1,*, Tomohiro Harada1,†, Ken-ichi Nakao2,‡, Pankaj S. Joshi3,§, and Masashi Kimura4,5,¶

  • 1Department of Physics, Rikkyo University, Toshima-ku, Tokyo 171-8501 Japan
  • 2Department of Mathematics and Physics, Graduate School of Science, Osaka City University, Osaka 558-8585, Japan
  • 3Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
  • 4DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, England CB3 0WA, United Kingdom
  • 5CENTRA, Departamento de Física, Instituto Superior Técnico–IST, Universidade de Lisboa–UL, Avenida Rovisco Pais 1, 1049 Lisboa, Portugal

  • *mandar@rikkyo.ac.jp, mandarppatil@gmail.com
  • harada@rikkyo.ac.jp
  • knakao@sci.osaka-cu.ac.jp
  • §psj@tifr.res.in
  • masashi.kimura@tecnico.ulisboa.pt

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Vol. 93, Iss. 10 — 15 May 2016

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