Skip to main content
Log in

New Bianchi type-I cosmological models for biharmonic particles using string cosmology with exponential law

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

Anisotropic Bianchi type-I magnetized string cosmological models are obtained in decaying vacuum energy density proposed by Pradhan (Commun Theor Phys 55:931–941, 2011). In this study, we obtain some physical and geometrical properties of biharmonic particles of a new spacetime using Bianchi type-I (B-I) cosmological model. We use solution of the Einstein’s field equations for biharmonic particles. Some important features of the model have been discussed. Established the existence of string cosmological models for biharmonic particles, unlike the earlier authors, in this theory and studied some physical and geometrical properties.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Adlav, K.S.: LRS Bianchi Type-I universe with anisotropic dark energy in lyra geometry. Int. J. Astron. Astrophys. 1, 204–209 (2011)

    Article  Google Scholar 

  2. Caltenco, J.H., Linares, R., López-Bonilla, J.L.: Intrinsic geometry of curves and the Lorentz equation. Czech. J. Phys. 52, 839–842 (2002)

    Article  ADS  Google Scholar 

  3. Capovilla, R., Chryssomalakos, C., Guven, J.: Hamiltonians for curves. J. Phys. A Math. Gen. 35, 6571–6587 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Carmeli, M.: Motion of a charge in a gravitational field. Phys. Rev. B 138, 1003–1007 (1965)

    Article  MathSciNet  ADS  Google Scholar 

  5. Deschamps, G.A.: Exterior Differential Forms. Springer, Berlin (1970)

    Google Scholar 

  6. Deschamps, G.A.: Electromagnetism and differential forms. IEEE Proc. 69, 676–696 (1981)

    Article  Google Scholar 

  7. Eells, J., Lemaire, L.: A report on harmonic maps. Bull. Lond. Math. Soc. 10, 1–68 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  8. Einstein, A.: Relativity: The Special and General Theory. Henry Holt, New York (1920)

    Google Scholar 

  9. Everett, A.E.: Cosmic strings ln unified gauge theories. Phys. Rev. 24, 858–868 (1981)

    ADS  Google Scholar 

  10. Hehl, F.W., Obhukov, Y.: Foundations of Classical Electrodynamics. Birkhauser, Basel (2003)

    Book  MATH  Google Scholar 

  11. Honig, E., Schucking, E., Vishveshwara, C.: Motion of charged particles in homogeneous electromagnetic fields. J. Math. Phys. 15, 774–781 (1974)

    Article  MathSciNet  ADS  Google Scholar 

  12. Jiang, G.Y.: 2-harmonic maps and their first and second variational formulas. Chin. Ann. Math. Ser. A 7(4), 389–402 (1986)

    MATH  Google Scholar 

  13. Kibble, T.W.B.: Topology of cosmic domains and strings. J. Phys. A Math. Gen. 9, 1387–1398 (1976)

    Article  ADS  MATH  Google Scholar 

  14. Kibble, T.W.B.: Some implications of a cosmological phase transition. Phys. Rep. 67(1), 183–199 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  15. Körpınar, T., Turhan, E.: Time-canal surfaces around biharmonic particles and its Lorentz transformations in Heisenberg spacetime. Int. J. Theor. Phys. 53, 1502–1520 (2014)

    Article  MATH  Google Scholar 

  16. Körpınar, T., Turhan, E.: On characterization of B-canal surfaces in terms of biharmonic B-slant helices according to Bishop frame in Heisenberg group Heis\(^{3}\). J. Math. Anal. Appl. 382, 57–65 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Körpınar, T., Turhan, E., Asil, V.: Tangent Bishop spherical images of a biharmonic B-slant helix in the Heisenberg group Heis\(^{3}\). Iran. J. Sci. Technol. Trans. A Sci. 35, 265–271 (2012)

    Google Scholar 

  18. Körpınar, T.: New characterizations for minimizing energy of biharmonic particles in Heisenberg spacetime. Int. J. Theor. Phys. 53, 3208–3218 (2014)

    Article  MATH  Google Scholar 

  19. Körpınar, T., Turhan, E.: Time-tangent surfaces around biharmonic particles and its Lorentz transformations in Heisenberg spacetime. Int. J. Theor. Phys. 52, 4427–4438 (2013)

    Article  MATH  Google Scholar 

  20. Körpınar, T., Turhan, E.: A new version of time-pencil surfaces around biharmonic particles and its Lorentz transformations in Heisenberg spacetime. Int. J. Theor. Phys. 53, 2288–2302 (2014)

    Article  MATH  Google Scholar 

  21. Körpınar, T., Turhan, E.: Bianchi Type-I cosmological models for biharmonic particles and its transformations in spacetime. Int. J. Theor. Phys. 54, 664–671 (2015)

    Article  Google Scholar 

  22. Letelier, P.S.: Clouds of strings in general relativity. Phys. Rev. D 20, 1294–1302 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  23. Letelier, P.S.: String cosmologies. Phys. Rev. D 28, 2414–2419 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  24. Maluf, J.W., Faria, F.F.: On the construction of Fermi–Walker transported frames. Ann. Phys. (Berlin) 17(5), 326–335 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. Misner, C.W.: The isotropy of the universe. Astrophys J. 151, 431–457 (1968)

    Article  ADS  Google Scholar 

  26. O’Neill, B.: Semi-Riemannian Geometry. Academic Press, New York (1983)

    MATH  Google Scholar 

  27. Pradhan, A., Singh, A.K.: Anisotropic Bianchi Type-I string cosmological models in normal gauge for Lyra’s manifold with constant deceleration parameter. Int. J. Theor. Phys. 50, 916–933 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. Pradhan, A., Singh, A.K., Amirhashchi, H.: A new class of Bianchi Type-I cosmological models in scalar-tensor theory of gravitation and late time acceleration. Int. J. Theor. Phys. 51, 3769–3786 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  29. Pradhan, A., Jaiswal, R., Khare, R.K.: Bianchi type-I cosmological models with time dependent \(q\) and \(\Lambda \)-term in general relativity. Astrophys. Space Sci. 343, 489–497 (2013)

    Article  ADS  MATH  Google Scholar 

  30. Pradhan, A.: Anisotropic Bianchi Type-I magnetized string cosmological models with decaying vacuum energy density. Commun. Theor. Phys. 55, 931–941 (2011)

  31. Stachel, J.: Thickening the string. I. The string perfect dust. Phys. Rev. D 21, 2171–2181 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  32. Synge, J.L.: Relativity: The General Theory. North Holland, Amsterdam (1960)

    MATH  Google Scholar 

  33. Turhan, E., Körpınar, T.: On characterization of timelike horizontal biharmonic curves in the Lorentzian Heisenberg Group Heis\(^{3}\). Zeitschrift für Naturforschung A J. Phys. Sci. 65a, 641–648 (2010)

    ADS  Google Scholar 

  34. Turhan, E., Körpınar, T.: Position vector of spacelike biharmonic curves in the Lorentzian Heisenberg group Heis\(^{3}\). Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica 19, 285–296 (2011)

    MATH  Google Scholar 

  35. Turhan, E., Körpınar, T.: On characterization canal surfaces around timelike horizontal biharmonic curves in Lorentzian Heisenberg Group Heis\(^{3}\). Zeitschrift für Naturforschung A J. Phys. Sci. 66a, 441–449 (2011)

    Article  ADS  Google Scholar 

  36. Vilenkin, A.: Cosmic strings. Phys. Rev. D 24, 2082–2089 (1981)

    Article  ADS  Google Scholar 

  37. Weber, J.: Relativity and Gravitation. Interscience, New York (1961)

    Google Scholar 

  38. Zel’dovich, Y.B.: Cosmological fluctuations near singularity. Mon. Not. R. Astron. Soc. 192, 663–667 (1980)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

The authors would like to express their sincere gratitude to the referee for valuable suggestions to improve the paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Talat Körpinar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Körpinar, T., Ünlütürk, Y. New Bianchi type-I cosmological models for biharmonic particles using string cosmology with exponential law. Gen Relativ Gravit 47, 138 (2015). https://doi.org/10.1007/s10714-015-1980-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-015-1980-7

Keywords

Navigation