The European Physical Journal C

, 71:1765 | Cite as

Repulsive Casimir–Polder forces from cosmic strings

  • A. A. SaharianEmail author
  • A. S. Kotanjyan
Regular Article - Theoretical Physics


We investigate the Casimir–Polder force acting on a polarizable microparticle in the geometry of a straight cosmic string. In order to develop this analysis we evaluate the electromagnetic field Green tensor on the imaginary frequency axis. The expression for the Casimir–Polder force is derived in the general case of anisotropic polarizability. In dependence on the eigenvalues for the polarizability tensor and of the orientation of its principal axes, the Casimir–Polder force can be either repulsive or attractive. Moreover, there are situations where the force changes the sign with separation. We show that for an isotropic polarizability tensor the force is always repulsive. At large separations between the microparticle and the string, the force varies inversely with the fifth power of the distance. In the non-retarded regime, corresponding to separations smaller than the relevant transition wavelengths, the force decays with the inverse fourth power of the distance. In the case of anisotropic polarizability, the dependence of the Casimir–Polder potential on the orientation of the polarizability tensor principal axes also leads to a moment of force acting on the particle.


Cosmic String Minkowski Spacetime Transverse Electric Polarizability Tensor Anisotropic Polarizability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    A. Vilenkin, E.P.S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, 1994) zbMATHGoogle Scholar
  2. 2.
    E.J. Copeland, T.W.B. Kibble, Proc. R. Soc. Lond. Ser. A 466, 623 (2010) MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. 3.
    V.M. Mostepanenko, N.N. Trunov, The Casimir Effect and Its Applications (Oxford University Press, Oxford, 1997) Google Scholar
  4. 4.
    E. Elizalde, S.D. Odintsov, A. Romeo, A.A. Bytsenko, S. Zerbini, Zeta Regularization Techniques with Applications (World Scientific, Singapore, 1994) zbMATHCrossRefGoogle Scholar
  5. 5.
    K.A. Milton, The Casimir Effect: Physical Manifestation of Zero-Point Energy (World Scientific, Singapore, 2002) Google Scholar
  6. 6.
    M. Bordag, G.L. Klimchitskaya, U. Mohideen, V.M. Mostepanenko, Advances in the Casimir Effect (Oxford University Press, Oxford, 2009) zbMATHCrossRefGoogle Scholar
  7. 7.
    E.R. Bezerra de Mello, V.B. Bezerra, A.A. Saharian, A.S. Tarloyan, Phys. Rev. D 74, 025017 (2006) ADSCrossRefGoogle Scholar
  8. 8.
    I. Brevik, T. Toverud, Class. Quantum Gravity 12, 1229 (1995) MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. 9.
    E.R. Bezerra de Mello, V.B. Bezerra, A.A. Saharian, Phys. Lett. B 645, 245 (2007) ADSCrossRefGoogle Scholar
  10. 10.
    E.R. Bezerra de Mello, V.B. Bezerra, A.A. Saharian, A.S. Tarloyan, Phys. Rev. D 78, 105007 (2008) ADSCrossRefGoogle Scholar
  11. 11.
    E.R. Bezerra de Mello, V.B. Bezerra, A.A. Saharian, V.M. Bardeghyan, Phys. Rev. D 82, 085033 (2010) ADSCrossRefGoogle Scholar
  12. 12.
    S. Bellucci, E.R. Bezerra de Mello, A.A. Saharian, Phys. Rev. D 83, 085017 (2011) ADSCrossRefGoogle Scholar
  13. 13.
    V.V. Nesterenko, G. Lambiase, G. Scarpetta, J. Math. Phys. 42, 1974 (2001) MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. 14.
    V.V. Nesterenko, I.G. Pirozhenko, J. Dittrich, Class. Quantum Gravity 20, 431 (2003) MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. 15.
    A.H. Rezaeian, A.A. Saharian, Class. Quantum Gravity 19, 3625 (2002) MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. 16.
    A.A. Saharian, Eur. Phys. J. C 52, 721 (2007) ADSCrossRefGoogle Scholar
  17. 17.
    A.A. Saharian, A.S. Tarloyan, Ann. Phys. 323, 1588 (2008) MathSciNetADSzbMATHCrossRefGoogle Scholar
  18. 18.
    A.A. Saharian, in The Casimir Effect and Cosmology (Volume in Honor of Professor Iver H. Brevik on the Occasion of His 70th Birthday), ed. by S.D. Odintsov et al. (Tomsk State Pedagogical University Press, Tomsk, 2008), p. 87. arXiv:0810.5207 Google Scholar
  19. 19.
    I. Brevik, S.A. Ellingsen, K.A. Milton, Phys. Rev. E 79, 041120 (2009) ADSCrossRefGoogle Scholar
  20. 20.
    S.A. Ellingsen, I. Brevik, K.A. Milton, Phys. Rev. E 80, 021125 (2009) ADSCrossRefGoogle Scholar
  21. 21.
    S.A. Ellingsen, I. Brevik, K.A. Milton, Phys. Rev. D 81, 065031 (2010) MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    G. Fucci, K. Kirsten, J. High Energy Phys. 1103, 016 (2011) ADSCrossRefMathSciNetGoogle Scholar
  23. 23.
    G. Fucci, K. Kirsten, J. Phys. A 44, 295403 (2011) CrossRefMathSciNetGoogle Scholar
  24. 24.
    E.R. Bezerra de Mello, A.A. Saharian, Class. Quantum Gravity 28, 145008 (2011) ADSCrossRefMathSciNetGoogle Scholar
  25. 25.
    V.A. Parsegian, Van der Waals forces: A Handbook for Biologists, Chemists, Engineers, and Physicists (Cambridge University Press, Cambridge, 2005) CrossRefGoogle Scholar
  26. 26.
    S.Y. Buhmann, D.-G. Welsch, Prog. Quantum Electron. 31, 51 (2007) ADSCrossRefGoogle Scholar
  27. 27.
    H. Friedrich, J. Trost, Phys. Rep. 397, 359 (2004) MathSciNetADSCrossRefGoogle Scholar
  28. 28.
    G.L. Klimchitskaya, U. Mohideen, V.M. Mostepanenko, Rev. Mod. Phys. 81, 1827 (2009) ADSCrossRefGoogle Scholar
  29. 29.
    K.A. Milton, E.K. Abalo, P. Parashar, N. Pourtolami, I. Brevik, S.A. Ellingsen, Phys. Rev. A 83, 062507 (2011) ADSCrossRefGoogle Scholar
  30. 30.
    V.M. Bardeghyan, A.A. Saharian, J. Contemp. Phys. 45, 1 (2010) CrossRefGoogle Scholar
  31. 31.
    G.E. Volovik, JETP Lett. 67, 698 (1998) ADSCrossRefGoogle Scholar
  32. 32.
    U.R. Fischer, M. Visser, Phys. Rev. Lett. 88, 110201 (2002) MathSciNetADSCrossRefGoogle Scholar
  33. 33.
    C. Sátiro, F. Moraes, Mod. Phys. Lett. A 20, 2561 (2005) ADSCrossRefGoogle Scholar
  34. 34.
    G.A. Korn, T.M. Korn, Mathematical Handbook for Scientists and Engineers (Dover, New York, 2000) Google Scholar
  35. 35.
    A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev, Integrals and Series, vol. 2 (Gordon and Breach, New York, 1986) Google Scholar
  36. 36.
    I. Brevik, M. Lygren, V.N. Marachevsky, Ann. Phys. (NY) 267, 134 (1998) ADSCrossRefGoogle Scholar
  37. 37.
    T.N.C. Mendez, F.S.S. Rosa, A. Tenório, C. Farina, J. Phys. A, Math. Theor. 41, 164020 (2008) ADSCrossRefGoogle Scholar
  38. 38.
    V.B. Bezerra, E.R. Bezerra de Mello, G.L. Klimchitskaya, V.M. Mostepanenko, A.A. Saharian, Eur. Phys. J. C 71, 1614 (2011) ADSCrossRefGoogle Scholar
  39. 39.
    E.R. Bezerra de Mello, A.A. Saharian, arXiv:1107.2557
  40. 40.
    M. Abramowitz, I.A. Stegun (eds.), Handbook of Mathematical Functions (Dover, New York, 1972) zbMATHGoogle Scholar
  41. 41.
    J. Spinelly, E.R. Bezerra de Mello, J. High Energy Phys. 0812, 081 (2008) MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2011

Authors and Affiliations

  1. 1.Department of PhysicsYerevan State UniversityYerevanArmenia

Personalised recommendations