Skip to main content
SpringerLink
Log in

Faraday Tensor for Time-Smarandache TN Particles Around Biharmonic Particles and its Lorentz Transformations in Heisenberg Spacetime

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

In this paper, we characterize time-Smarandache particle around timelike biharmonic particle in \(\mathcal {H}_{1}^{4}.\) Moreover, we obtain Lorentz transformations this particles. Finally, we construct electric and magnetic fields of time-Smarandache particle with constant curvature.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baumgarte, T.W., Shapiro, S.L.: General Relativistic Magnetohydrodyamics For The Numerical Construction Of Dynamical Spacetimes. Astrophys. J. 585, 921–929 (2003)

    Article  ADS  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  MATH  ADS  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. Gray, A.: Modern Differential Geometry of Curves and Surfaces with Mathematica. CRC Press (1998)

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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

    Book  MATH  Google Scholar 

  10. 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 

  11. 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 

  12. Körpınar, T., Turhan: Time-canal surfaces around Biharmonic particles and its Lorentz transformations in Heisenberg spacetime. Int. J. Theor. Phys. 53, 1502–1520 (2013)

    Article  Google Scholar 

  13. Körpınar, T., Turhan: 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 (2012)

    Article  Google Scholar 

  14. 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 

  15. 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 http://dx.doi.org/10.1007/s10773-014-2029-5 (2014)

  16. 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 

  17. Mashhoong, B.: Gravitoelectromagnetism, arXiv:gr-qc/0011014v1

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

    MATH  Google Scholar 

  19. Pina, E.: Lorentz transformation and the motion of a charge in a constant electromagnetic field. Rev. Mex. Fis 16, 233–236 (1967)

    Google Scholar 

  20. Ringermacher, H.: Intrinsic geometry of curves and the Minkowski force. Phys. Lett. A 74, 381–383 (1979)

    Article  MathSciNet  ADS  Google Scholar 

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

  22. Synge, J.L.: Time-like helices in flat spacetime. Proc. R. Ir. Acad., Sect. A 65, 27–41 (1967)

    MathSciNet  MATH  Google Scholar 

  23. Trocheris, M.G.: Electrodynamics in a rotating frame of reference. Philo. Mag. 7, 1143–1155 (1949)

    MathSciNet  Google Scholar 

  24. Turhan, E., Körpınar, T.: On characterization of timelike horizontal Biharmonic curves in the Lorentzian Heisenberg group Heis 3.. Z. für Naturforsch. A- A J. Phys. Sci. 65a, 641–648 (2010)

    Google Scholar 

  25. Turhan, E., Körpınar, T.: Position vector of spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3. An. St. Univ. Ovidius Constanta, Ser. Mat. 19, 285–296 (2011)

    MATH  Google Scholar 

  26. Turhan, E., Körpınar, T.: On characterization canal surfaces around timelike horizontal Biharmonic curves in Lorentzian Heisenberg group Heis 3. Z. für Naturforsch. A- A J. Phys. Sci. 66a, 441–449 (2011)

    Article  Google Scholar 

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

    Google Scholar 

Download references

Acknowledgments

The author would like to express their sincere gratitude to the referees for the valuable suggestions to improve the paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, Muş Alparslan University, 49250, Muş, Turkey

    Talat Körpinar

Authors
  1. Talat Körpinar
    View author publications

    You can also search for this author in PubMed Google Scholar

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. Faraday Tensor for Time-Smarandache TN Particles Around Biharmonic Particles and its Lorentz Transformations in Heisenberg Spacetime. Int J Theor Phys 53, 4153–4159 (2014). https://doi.org/10.1007/s10773-014-2166-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-014-2166-x

Keywords

Search

Navigation