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Gravitation and Cosmology

, Volume 14, Issue 1, pp 28–37 | Cite as

New branches of electrically charged Einstein-Yang-Mills-Higgs solutions

  • R. Ibadov
  • B. Kleihaus
  • J. Kunz
  • U. Neemann
Article
  • 37 Downloads

Abstract

We consider dyons and electrically charged monopole-antimonopole pairs in Einstein-Yang-Mills-Higgs theory. In the presence of an electric charge, bifurcations arise and new branches of solutions appear. For large values of the electric charge, spherically symmetric dyons approach limiting solutions related to the Penney solution of Einstein-Maxwell-scalar theory.

PACS numbers

04.20.Jb 04.40.Nr 

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References

  1. 1.
    G. ‘t Hooft, Nucl. Phys. B 79, 276 (1974); A. M. Polyakov, Pis’ma JETP 20, 430 (1974).ADSCrossRefGoogle Scholar
  2. 2.
    E. J. Weinbergand, A. H. Guth, Phys.Rev. D 14, 1660 (1976).ADSCrossRefGoogle Scholar
  3. 3.
    C. Rebbi and P. Rossi, Phys. Rev. D 22, 2010 (1980).ADSCrossRefGoogle Scholar
  4. 4.
    R. S. Ward, Commun. Math. Phys. 79, 317 (1981); P. Forgacs, Z. Horvath, and L. Palla, Phys. Lett. 99B, 232 (1981);M. K. Prasad, Commun.Math. Phys. 80, 137 (1981); M. K. Prasad and P. Rossi, Phys. Rev. D 24, 2182 (1981).ADSCrossRefGoogle Scholar
  5. 5.
    B. Kleihaus, J. Kunz, and D. H. Tchrakian, Mod. Phys. Lett. A 13, 2523 (1998).ADSCrossRefMathSciNetGoogle Scholar
  6. 6.
    N. J. Hitchin, N. S. Manton, and M. K. Murray, Nonlinearity 8, 661 (1995); C. J. Houghton and P. M. Sutcliffe, Commun. Math. Phys. 180, 343 (1996); C. J. Houghton and P. M. Sutcliffe, Nonlinearity 9, 385 (1996); P.M. Sutcliffe, Int. J. Mod. Phys. A 12, 4663 (1997); C. J. Houghton, N. S. Manton, and P. M. Sutcliffe, Nucl. Phys. B 510, 507 (1998).ADSCrossRefMathSciNetGoogle Scholar
  7. 7.
    C. H. Taubes, Commun. Math. Phys. 86, 257 (1982); 86, 299 (1982); 97, 473 (1985).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    W. Nahm, unpublished; B. Ruüber, PhD thesis (University of Bonn, 1985).Google Scholar
  9. 9.
    B. Kleihaus and J. Kunz, Phys. Rev. D 61, 025003 (2000).ADSCrossRefMathSciNetGoogle Scholar
  10. 10.
    B. Kleihaus, J. Kunz, and Ya. Shnir, Phys. Lett. 570B, 237 (2003); Phys. Rev. D 68, 101701(R) (2003); Phys. Rev. D 70, 065010 (2004).CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    J. Kunz, U. Neemann, and Ya. Shnir, Phys. Lett. 640B, 57 (2006).CrossRefzbMATHGoogle Scholar
  12. 12.
    B. Julia and A. Zee, Phys. Rev. D 11, 2227 (1975); M. K. Prasad and C.M. Sommerfeld, Phys. Rev. Lett. 35, 760 (1975).ADSGoogle Scholar
  13. 13.
    B. Hartmann, B. Kleihaus, and J. Kunz, Mod. Phys. Lett. A 15, 1003 (2000).ADSCrossRefGoogle Scholar
  14. 14.
    M. Heusler, N. Straumann, and M. Volkov, Phys.Rev. D 58, 105021 (1998).MathSciNetGoogle Scholar
  15. 15.
    J. J. van der Bij and E. Radu, Int. J.Mod. Phys. A 17, 1477 (2002); 18, 2379 (2003).ADSCrossRefzbMATHGoogle Scholar
  16. 16.
    K. Lee, V. P. Nair, and E. J. Weinberg, Phys. Rev. D 45, 2751 (1992); P. Breitenlohner, P. Forgacs, and D. Maison, Nucl. Phys. B 383, 357 (1992); 442, 126 (1995).ADSzbMATHMathSciNetGoogle Scholar
  17. 17.
    Y. Brihaye, B. Hartmann, and J. Kunz, Phys. Lett. 441B, 77 (1998); Y. Brihaye, B. Hartmann, J. Kunz, andN. Tell,Phys. Rev. D 60, 104016 (1999).CrossRefMathSciNetGoogle Scholar
  18. 18.
    B. Hartmann, B. Kleihaus, and J. Kunz, Phys. Rev. Lett. 86, 1422 (2001); Phys. Rev. D 65, 024027 (2001).ADSCrossRefGoogle Scholar
  19. 19.
    B. Kleihaus and J. Kunz, Phys. Rev. Lett. 85, 2430 (2000).ADSCrossRefGoogle Scholar
  20. 20.
    V. Paturyan, E. Radu, and D. H. Tchrakian, Phys. Lett. 609B, 360 (2005).CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    B. Kleihaus, J. Kunz, and U. Neemann, Phys. Lett. 623B, 171 (2005).CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    B. Kleihaus, J. Kunz, F. Navarro-Lérida, and U. Neemann, arXiv: 0705.1511 [gr-qc].Google Scholar
  23. 23.
    B. Kleihaus, J. Kunz, and Ya. Shnir, Phys. Rev. D 71, 024013 (2005); J. Kunz, U. Neemann, and Ya. Shnir, Phys. Rev. D 75, 125008 (2007).ADSGoogle Scholar
  24. 24.
    For n = 1dyonswith a vanishingHiggs potential, this branch does notmerge with the RNbranch, but with a short second non-Abelian branch, which then merges with the RN branch [16].Google Scholar
  25. 25.
    As the non-Abelian branch merges with the RN branch, the space-time splits into interior and exterior regions, where, in the exterior region, the limiting solution corresponds to the extremal RN solution, whereas in the interior region the solution retains its non-Abelian character [16, 18].Google Scholar
  26. 26.
    R. Bartnik and J. McKinnon, Phys. Rev. Lett. 61, 141 (1988).ADSCrossRefMathSciNetGoogle Scholar
  27. 27.
    B. Kleihaus and J. Kunz, Phys. Rev. Lett. 78, 2527 (1997); Phys. Rev. D 57, 834 (1998).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    R. Ibadov, B. Kleihaus, J. Kunz, and Ya. Shnir, Phys. Lett. 609B, 150 (2005).CrossRefzbMATHMathSciNetGoogle Scholar
  29. 29.
    R. Ibadov, B. Kleihaus, J. Kunz, and U. Neemann, Phys. Lett. B 659, 421 (2008).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    R. Penney, Phys. Rev. 182, 1383 (1969).ADSCrossRefMathSciNetGoogle Scholar
  31. 31.
    B. Kleihaus and J. Kunz, Phys. Rev. Lett. 86, 3704 (2001); B. Kleihaus, J. Kunz, and F. Navarro-Le´ rida, Phys. Rev. D 66, 104001 (2002).ADSCrossRefMathSciNetGoogle Scholar
  32. 32.
    B. Kleihaus, J. Kunz and F. Navarro-Lérida, Phys. Lett. 599B, 294 (2004).CrossRefzbMATHMathSciNetGoogle Scholar
  33. 33.
    W. Scho¨ nauer and R. Weiß, J. Comput. Appl. Math. 27, 279 (1989); M. Schauder, R. Weiß, and W. Scho¨ nauer, The CADSOL Program Package, Universita¨ t Karlsruhe, Interner Bericht Nr. 46/92 (1992).CrossRefGoogle Scholar
  34. 34.
    Expanding the solution H 2() of the Yang-Mills equation (30) in a power series, H 2() = 1+h 1 + h 2 2/2 + O( 3), shows that h 1 = 0 while h 2 is a free parameter, characterizing the solution. Solving the equation numerically in the interval 0 ≤ ≤ 1 with the boundary conditions H 2(0) = 1, H 2(1) = h *, and varying h *, we observe that h 2(h *) increases with increasing h *. and tends to a finite value h 2max ≈ 3.047 when h * tends to infinity. In comparison with the numerical dyon solutions for a large charge Q, we find some evidence that H 2 (0) indeed tends to the value h 2max for Q → ∞ i.e., H2 diverges at = 1 in the limit. The convergence is, however, very slow, approximately like \(1/\sqrt Q \) Google Scholar
  35. 35.
    A. A. Ershov and D. V. Galtsov, Phys. Lett. 150A, 159 (1990).ADSCrossRefMathSciNetGoogle Scholar
  36. 36.
    P. Bizon and O. T. Popp, Class.Quantum Grav. 9, 193 (1992).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  37. 37.
    B. Kleihaus, J. Kunz, and K. Myklevoll, Phys. Lett. 632B, 333 (2006).CrossRefMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  • R. Ibadov
    • 1
  • B. Kleihaus
    • 2
  • J. Kunz
    • 3
  • U. Neemann
    • 3
  1. 1.Department of Theoretical Physics and Computer ScienceSamarkand State UniversitySamarkandUzbekistan
  2. 2.ZARMUniversität BremenBremenGermany
  3. 3.Institut für PhysikUniversität OldenburgOldenburgGermany

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