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Gravitation and Cosmology

, Volume 15, Issue 3, pp 241–246 | Cite as

Wormholes supported by chiral fields

  • K. A. BronnikovEmail author
  • S. V. Chervon
  • S. V. Sushkov
Article

Abstract

We consider static, spherically symmetric solutions of general relativity with a non-linear sigma model (NSM) as a source, i.e., a set of scalar fields Φ = (Φ1, …, Φ n ) (so-called chiral fields) parametrizing a target space with a metric h ab (Φ). For NSM with zero potential V (Φ), it is shown that the space-time geometry is the same as with a single scalar field but depends on h ab . If the matrix h ab is positive-definite, we obtain the Fisher metric, originally found for a canonical scalar field with positive kinetic energy; otherwise we obtain metrics corresponding to a phantom scalar field, including singular and nonsingular horizons (of infinite area) and wormholes. In particular, the Schwarzschild metric can correspond to a nontrivial chiral field configuration, which in this case has zero stress-energy. Some explicit examples of chiral field configurations are considered. Some qualitative properties of NSM configurations with nonzero potentials are pointed out.

PACS numbers

04.20.-q 04.20.Jb 04.40.-b 

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References

  1. 1.
    I. Z. Fisher, Zh. Eksp. Teor. Fiz. 18, 636 (1948); grqc/9911008.Google Scholar
  2. 2.
    S. V. Chervon, Nonlinear Fields in Theory of Gravitation and Cosmology (Middle-Volga Scientific Centre, Ulyanovsk State University, Ulyanovsk, 1997).Google Scholar
  3. 3.
    O. Bergmann and R. Leipnik, Phys. Rev. 107, 1157 (1957).CrossRefMathSciNetADSGoogle Scholar
  4. 4.
    H. Yilmaz, Phys. Rev. 111, 1417 (1958).zbMATHCrossRefMathSciNetADSGoogle Scholar
  5. 5.
    H. A. Buchdahl, Phys. Rev. 115, 1325 (1959).zbMATHCrossRefMathSciNetADSGoogle Scholar
  6. 6.
    A. I. Janis, D. C. Robinson, and J. Winicour, Phys. Rev. 186, 1729 (1969).CrossRefADSGoogle Scholar
  7. 7.
    H. Ellis, J.Math. Phys. 14, 104 (1973).CrossRefADSGoogle Scholar
  8. 8.
    K. A. Bronnikov, Acta Phys. Pol. B 4, 251 (1973).MathSciNetGoogle Scholar
  9. 9.
    M. Wyman, Phys. Rev. D 24, 839 (1981).CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    C. Armendáriz-Picón, Phys. Rev. D 65, 104 010 (2002).Google Scholar
  11. 11.
    S. V. Sushkov and Y.-Z. Zhang, Phys. Rev. D 77, 024042 (2008).Google Scholar
  12. 12.
    A. R. Liddle and D. H. Lyth, Cosmological Inflation and Large-Scale Structure (Cambridge University Press, 2000).Google Scholar
  13. 13.
    A. M. Perelomov, Phys. Rep. 146(3), 136 (1987).CrossRefMathSciNetADSGoogle Scholar
  14. 14.
    J. Schwinger, Ann. Phys. 2, 407 (1957).zbMATHCrossRefMathSciNetADSGoogle Scholar
  15. 15.
    T. H. R. Skyrme, Proc. Roy. Soc. Lond. A 247(1249), 260 (1958).CrossRefADSGoogle Scholar
  16. 16.
    M. Gell-Mann and M. Levy, Nuovo Cim. 26(4), 705 (1960).CrossRefMathSciNetGoogle Scholar
  17. 17.
    V. De Alfaro, S. Fubini, and G. Furlan, Nuovo Cim. A 50, 523 (1979).CrossRefADSGoogle Scholar
  18. 18.
    G. G. Ivanov, Teor. Mat. Fiz. 57, 45 (1983).Google Scholar
  19. 19.
    S. V. Chervon, Izv. Vuzov, Fiz. (Russ. Phys. J., New York) 26(8), 89 (1983).Google Scholar
  20. 20.
    S. V. Chervon, Grav. Cosmol. 1, 91 (1995).zbMATHADSGoogle Scholar
  21. 21.
    S. V. Chervon, Grav. Cosmol. 3, 145 (1997).zbMATHADSGoogle Scholar
  22. 22.
    V. D. Ivashchuk and V. N. Melnikov, Exact Solutions in Multidimensional Gravity with Antisymmetric Forms, Topical Review. Class. Quantum Grav. 18, R87–R152 (2001); hep-th/0110274.MathSciNetGoogle Scholar
  23. 23.
    M. S. Morris and K. S. Thorne, Am. J. Phys. 56, 395 (1988).CrossRefMathSciNetADSGoogle Scholar
  24. 24.
    D. Hochberg and M. Visser, Phys. Rev. D 56, 4745 (1997).CrossRefMathSciNetADSGoogle Scholar
  25. 25.
    K. A. Bronnikov, M. S. Chernakova, J. C. Fabris, N. Pinto-Neto and M. E. Rodrigues, Int. J. Mod. Phys. D 17, 25 (2008); gr-qc/0609084.zbMATHCrossRefMathSciNetADSGoogle Scholar
  26. 26.
    K. A. Bronnikov and S.G. Rubin, Lectures on Gravitation and Cosmology (MIFI Press, Moscow, 2008, in Russian).Google Scholar
  27. 27.
    S. V. Chervon, J. Astroph. Astron. 16,Suppl. 65 (1995).Google Scholar
  28. 28.
    K. A. Bronnikov, S. B. Fadeev, and A. V. Michtchenko, Gen. Rel. Grav. 35, 505 (2003); grqc/0212065.zbMATHCrossRefMathSciNetADSGoogle Scholar
  29. 29.
    S. Adler and R. B. Pearson, Phys. Rev. D 18, 2798 (1978).CrossRefMathSciNetADSGoogle Scholar
  30. 30.
    K. A. Bronnikov, Phys. Rev. D 64, 064013 (2001); grqc/0104092.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • K. A. Bronnikov
    • 1
    • 2
    Email author
  • S. V. Chervon
    • 3
    • 4
  • S. V. Sushkov
    • 5
    • 6
  1. 1.Center of Gravitation and Fundamental MetrologyVNIIMSMoscowRussia
  2. 2.Institute of Gravitation and CosmologyPFURMoscowRussia
  3. 3.Department of Theoretical PhysicsUlyanovsk State UniversityUlyanovskRussia
  4. 4.Department of General PhysicsUlyanovsk State Pedagogical UniversityUlyanovskRussia
  5. 5.Department of General Relativity and GravitationKazan State UniversityKazanRussia
  6. 6.Department of MathematicsTatar State University of Humanities and EducationKazanRussia

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