Physics of Particles and Nuclei Letters

, Volume 11, Issue 7, pp 890–893 | Cite as

Spherical mechanics for a particle near the horizon of extremal black hole

Article

Abstract

We describe canonical transformation, which links the Hamiltonian of a massive relativistic particle moving near the horizon of an extremal black hole to the conventional form of the conformal mechanics. Thus, like the non-relativistic conformal mechanics, the investigation of the particle dynamics reduces to analyzing its “spherical sector” defined by the Casimir element of the conformal algebra. We present a detailed list of such systems originating from various types of black hole configurations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Galajinsky and A. Nersessian, “Conformal mechanics inspired by extremal black holes in d = 4,” JHEP 1111, 135 (2011), arXiv:1108.3394 [hep-th].ADSCrossRefMathSciNetGoogle Scholar
  2. 2.
    A. Galajinsky, A. Nersessian, and A. Saghatelian, “Superintegrable models related to near horizon extremal Myers-Perry black hole in arbitrary dimension,” JHEP 1306, 002 (2013).ADSCrossRefMathSciNetGoogle Scholar
  3. 3.
    A. Galajinsky, A. Nersessian, and A. Saghatelian, “Action-angle variables for spherical mechanics related to near horizon extremal Myers-Perry black hole,” J. Phys. Conf. Ser. 474, 012019 (2013).ADSCrossRefGoogle Scholar
  4. 4.
    S. Bellucci, A. Galajinsky, E. Ivanov, and S. Krivonos, “AdS(2)/CFT(1), canonical transformations and superconformal mechanics,” Phys. Lett., Ser. B 555, 99 (2003).ADSCrossRefMATHGoogle Scholar
  5. 5.
    A. Galajinsky, “Particle dynamics on AdS(2) × S**2 background with two-form flux,” Phys. Rev., Ser. D 78, 044014 (2008).ADSCrossRefMathSciNetGoogle Scholar
  6. 6.
    T. Hakobyan, A. Nersessian, and V. Yeghikyan, “Cuboctahedric Higgs oscillator from the Calogero model,” J. Phys., Ser. A 42, 205206 (2009).ADSCrossRefMathSciNetGoogle Scholar
  7. 7.
    T. Hakobyan, S. Krivonos, O. Lechtenfeld, and A. Nersessian, “Hidden symmetries of integrable conformal mechanical systems,” Phys. Lett., Ser. A 374, 801 (2010).ADSCrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    O. Lechtenfeld, A. Nersessian, and V. Yeghikyan, “Action-angle variables for dihedral systems on the circle,” Phys. Lett., Ser. A 374, 4647 (2010).ADSCrossRefMathSciNetMATHGoogle Scholar
  9. 9.
    T. Hakobyan, O. Lechtenfeld, A. Nersessian, and A. Saghatelian, “Invariants of the spherical sector in conformal mechanics,” J. Phys., Ser. A 44, 055205 (2011).ADSCrossRefMathSciNetGoogle Scholar
  10. 10.
    T. Hakobyan, O. Lechtenfeld, and A. Nersessian, “The spherical sector of the Calogero model as a reduced matrix model,” Nucl. Phys., Ser. B 858, 250 (2012).ADSCrossRefMathSciNetMATHGoogle Scholar
  11. 11.
    V. I. Arnold, Mathematical Methods in Classical Mechanics (Nauka Publ., Moscow, 1973).Google Scholar
  12. 12.
    T. Hakobyan, O. Lechtenfeld, A. Nersessian, et al., “Integrable generalizations of oscillator and Coulomb systems via action-angle variables,” Phys. Lett., Ser. A 376, 679 (2012).ADSCrossRefMathSciNetMATHGoogle Scholar
  13. 13.
    A. Galajinsky, “Particle dynamics near extreme Kerr throat and supersymmetry,” JHEP 1011, 126 (2010). S. Bellucci, A. Nersessian, and V. Yeghikyan, “Actionangle variables for the particle near extreme Kerr throat,” Mod. Phys. Lett., Ser. A 27, 1250191 (2012).ADSCrossRefMathSciNetGoogle Scholar
  14. 14.
    A. Saghatelian, “Constants of motion of the four-particle Calogero model,” Class. Quant. Grav. 29, 245018 (2012).ADSCrossRefMathSciNetGoogle Scholar
  15. 15.
    G. Clément and D. Gal’tsov, “Bertotti-Robinson type solutions to dilaton-axion gravity,” Phys. Rev., Ser. D 63, 124011 (2001).CrossRefGoogle Scholar
  16. 16.
    B. Carter, “Hamilton-Jacobi and Schrodinger separable solutions of Einstein’s equations,” Commun. Math. Phys. 10, 280 (1968).MATHGoogle Scholar
  17. 17.
    T. Hartman, K. Murata, T. Nishioka, and A. Strominger, “CFT duals for extreme black holesm” JHEP 0904, 019 (2009).ADSCrossRefMathSciNetGoogle Scholar
  18. 18.
    A. Galajinsky and K. Orekhov, “N = 2 superparticle near horizon of extreme Kerr-Newman-AdS-dS black hole,” Nucl. Phys., Ser. B 850, 339 (2011).ADSCrossRefMathSciNetMATHGoogle Scholar
  19. 19.
    S. W. Hawking, C. J. Hunter, and M. M. Taylor-Robinson, “Rotation and the AdS/CFT correspondence,” Phys. Rev., Ser. D 59, 064005 (1999).ADSCrossRefMathSciNetGoogle Scholar
  20. 20.
    H. Lu, J. Mei, and C. N. Pope, “Kerr/CFT correspondence in diverse dimensions,” JHEP 0904, 054 (2009).ADSCrossRefMathSciNetGoogle Scholar
  21. 21.
    A. Galajinsky, “Near horizon black holes in diverse dimensions and integrable models,” Phys. Rev., Ser. D 87, 024023 (2013).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Tomsk Polytechnic UniversityTomskRussia
  2. 2.Yerevan State UniversityYerevanArmenia

Personalised recommendations