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Theoretical and Mathematical Physics

, Volume 190, Issue 2, pp 268–278 | Cite as

Black holes and particles with zero or negative energy

  • A. A. GribEmail author
  • Yu. V. Pavlov
Article

Abstract

We study properties of particles with zero or negative energy and a nonzero orbital angular momentum in the ergosphere of a rotating black hole. We show that the sign of the particle energy is uniquely determined by the angular velocity of its rotation in the ergosphere. We give a simple proof of the fact that extreme black holes cannot exist. We investigate the question of the possibility of an unlimited energy increase in the center-of-mass system of two colliding particles, one or both of which have negative or zero energy.

Keywords

black hole Kerr metric negative-energy particle particle collision geodesic 

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References

  1. 1.
    C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, Freeman, San Francisco (1973).Google Scholar
  2. 2.
    S. Chandrasekhar, The Mathematical Theory of Black Holes, Clarendon, Oxford (1983).zbMATHGoogle Scholar
  3. 3.
    I. D. Novikov and V. P. Frolov, Black Hole Physics [in Russian], Nauka, Moscow (1986)Google Scholar
  4. 3a.
    V. P. Frolov and I. D. Novikov, Black Hole Physics: Basic Concepts and New Developments, Kluwer, Dordrecht (1998).CrossRefzbMATHGoogle Scholar
  5. 4.
    A. A. Grib, Yu. V. Pavlov, and V. D. Vertogradov, “Geodesics with negative energy in the ergosphere of rotating black holes,” Modern Phys. Lett. A, 29, 1450110 (2014); arXiv:1304.7360v2 [gr-qc] (2013).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. 5.
    R. P. Kerr, “Gravitational field of a spinning mass as an example of algebraically special metrics,” Phys. Rev. Lett., 11, 237–238 (1963).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 6.
    R. H. Boyer and R. W. Lindquist, “Maximal analytic extension of the Kerr metric,” J. Math. Phys., 8, 265–281 (1967).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. 7.
    L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields [in Russian], Nauka, Moscow (1988); English transl. prev. ed., Pergamon, Oxford (1983).zbMATHGoogle Scholar
  9. 8.
    A. A. Grib and Yu. V. Pavlov, “Particles with negative energies in black holes,” Internat. J. Modern Phys. D, 20, 675–684 (2011).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. 9.
    A. A. Grib and Yu. V. Pavlov, “On the energy of particle collisions in the ergosphere of the rotating black holes,” Europhys. Lett., 101, 20004 (2013); arXiv:1301.0698v1 [gr-qc] (2013).ADSCrossRefGoogle Scholar
  11. 10.
    A. A. Grib and Yu. V. Pavlov, “Collision energy of particles in the ergosphere of rotating black holes,” Theor. Math. Phys., 176, 881–887 (2013).MathSciNetCrossRefzbMATHGoogle Scholar
  12. 11.
    O. B. Zaslavskii, “Acceleration of particles as a universal property of ergosphere,” Modern Phys. Lett. A, 28, 1350037 (2013).ADSCrossRefGoogle Scholar
  13. 12.
    K. S. Thorne, “Disk-accretion onto a black hole: II. Evolution of the hole,” Astrophys. J., 191, 507–519 (1974).ADSCrossRefGoogle Scholar
  14. 13.
    A. A. Grib and Yu. V. Pavlov, “On particles collisions near rotating black holes,” Grav. Cosmol., 17, 42–46 (2011).ADSCrossRefzbMATHGoogle Scholar
  15. 14.
    J. M. Bardeen, B. Carter, and S. W. Hawking, “The four laws of black hole mechanics,” Commun. Math. Phys., 31, 161–170 (1973).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. 15.
    A. P. Lightman, W. H. Press, R. H. Price, and S. A. Teukolsky, Problem Book in Relativity and Gravitation, Princeton Univ. Press, Princeton, N. J. (1975).zbMATHGoogle Scholar
  17. 16.
    J. M. Bardeen, W. H. Press, and S. A. Teukolsky, “Rotating black holes: Locally nonrotating frames, energy extraction, and scalar synchrotron radiation,” Astrophys. J., 178, 347–369 (1972).ADSCrossRefGoogle Scholar
  18. 17.
    M. Banados, J. Silk, and S. M. West, “Kerr black holes as particle accelerators to arbitrarily high energy,” Phys. Rev. Lett., 103, 111102 (2009).ADSCrossRefGoogle Scholar
  19. 18.
    A. A. Grib and Yu. V. Pavlov, “On particles collisions in the vicinity of rotating black holes,” JETP Letters, 92, 125–129 (2010).ADSCrossRefGoogle Scholar
  20. 19.
    A. A. Grib and Yu. V. Pavlov, “On particle collisions in the gravitational field of the Kerr black hole,” Astropart. Phys., 34, 581–586 (2011).ADSCrossRefGoogle Scholar
  21. 20.
    A. A. Grib and Yu. V. Pavlov, “Are black holes totally black?” Grav. Cosmol., 21, 13–18 (2015).Google Scholar
  22. 21.
    A. A. Grib and Yu. V. Pavlov, “High energy physics in the vicinity of rotating black holes,” Theor. Math. Phys., 185, 1425–1432 (2015).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Herzen State Pedagogical University of RussiaSt. PetersburgRussia
  2. 2.Friedmann Laboratory for Theoretical PhysicsSt. PetersburgRussia
  3. 3.Institute of Problems of Mechanical Engineering RASSt. PetersburgRussia
  4. 4.Lobachevsky Institute of Mathematics and MechanicsKazan Federal UniversityKazanRussia

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