Skip to main content
SpringerLink
Log in

Mathematical modeling of the nonlinear electrodynamics effect of signal delay in the magnetic field of pulsars

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

The paper is devoted to mathematical modeling of the nonlinear vacuum electrodynamics effect: the action of the strong magnetic field of a pulsar on the propagation of electromagnetic waves. It is shown that, due to the birefringence of the vacuum, for one normal wave, it takes more time to travel from a pulsar to a detector installed on astrophysical satellites than for the other normal wave. The delay of the pulse carried by the second normal wave relative to pulse carried by the first normal wave from the common point of origin to the satellite is calculated.

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. D. L. Burke, R. C. Feld, and G. Horton-Smith, “Positron production in multiphoton light-by-light,” Phys. Rev. Lett. 79 (9), 1626–1629 (1997).

    Article  Google Scholar 

  2. M. Born, Atomic Physics, 8th ed. (Mir, Moscow, 1965; Hafner, New York, 1969).

    Google Scholar 

  3. I. M. Ternov, V. R. Khalilov, and V. N. Rodionov, Interaction of Charged Particles with a Strong Electromagnetic Field (Mosk. Gos. Univ., Moscow, 1982) [in Russian].

    Google Scholar 

  4. V. I. Denisov, I. P. Denisova, and I. V. Krivchenkov, “Hamilton–Jacobi equation for fermions interacting nonminimally with electromagnetic field,” Dokl. Phys. 48 (7), 325–327 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  5. V. R. Khalilov, “Nonlinear effects induced by vacuum polarization by a strong electromagnetic field in a weak static electromagnetic field,” Theor. Math. Phys. 135 (2), 659–672 (2003).

    Article  MathSciNet  Google Scholar 

  6. V. I. Denisov and V. A. Sokolov, “Analysis of regularizing properties of nonlinear electrodynamics in the Einstein–Born–Infeld theory,” J. Exp. Theor. Phys. 113 (6), 926–933 (2011).

    Article  Google Scholar 

  7. N. N. Rozanov, “On self-action of intense electromagnetic radiation in electron-positron vacuum,” Zh. Eksp. Teor. Fiz. 113, 513–520 (1998).

    Google Scholar 

  8. V. I. Denisov and I. P. Denisova, “Interaction effect of plane electromagnetic waves in the Born–Infeld nonlinear electrodynamics,” Theor. Math. Phys. 129 (1), 1421–1427 (2001).

    Article  MATH  Google Scholar 

  9. V. R. Khalilov, Electrons in Strong Electromagnetic Fields: An Advanced Classical and Quantum Treatment (Energoatomizdat, Moscow, 1988; Routledge, London, 1996).

    Google Scholar 

  10. V. I. Denisov and I. P. Denisova, “Verifiable Post-Maxwellian Effect of the Nonlinear Electrodynamics in Vacuum,” Opt. Spectrosc. 90 (2), 282–287 (2001).

    Article  Google Scholar 

  11. V. I. Denisov and I. P. Denisova, “Interaction of intense laser radiation with weak electromagnetic waves in an evacuated section of a ring laser,” Opt. Spectrosc. 90 (6), 928–930 (2001).

    Article  MathSciNet  Google Scholar 

  12. P. A. Vshivtseva, V. I. Denisov, and I. P. Denisova, “Nonlinear electrodynamic effect of frequency doubling in the field of a magnetic dipole,” Dokl. Phys. 47 (11), 798–800 (2002).

    Article  MATH  Google Scholar 

  13. V. I. Denisov and S. I. Svertilov, “Nonlinear electromagnetic and gravitational actions of neutron star fields on electromagnetic wave propagation,” Phys. Rev. D Part. Fields 71 (6), 063002–063015 (2005).

    Article  Google Scholar 

  14. K. J. Nordtvedt, “Anisotropic parameterized post-Newtonian gravitational metric field,” Phys. Rev. D Part. Fields 14, 1511–1517 (1976).

    Article  Google Scholar 

  15. V. I. Denisov and I. P. Denisova, “The Eikonal equation in parametrized nonlinear electrodynamics of vacuum,” Dokl. Phys. 46 (6), 377–379 (2001).

    Article  MathSciNet  Google Scholar 

  16. V. I. Denisov, “Investigation of the effective space-time of the vacuum nonlinear electrodynamics in a magnetic dipole field,” Theor. Math. Phys. 132 (2), 1071–1079 (2002).

    Article  MATH  Google Scholar 

  17. P. A. Vshivtseva and M. M. Denisov, “Mathematical modeling of electromagnetic wave propagation in nonlinear electrodynamics,” Comput. Math. Math. Phys. 49 (12), 2092–2102 (2009).

    Article  MathSciNet  Google Scholar 

  18. V. I. Denisov and M. I. Denisov, “Verification of Einstein’s principle of equivalence using a laser gyroscope in terrestrial conditions,” Phys. Rev. D Part. Fields 60 (4), 047301 (1999).

    Article  MathSciNet  Google Scholar 

  19. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972).

    Google Scholar 

  20. V. I. Denisov, “Nonlinear effect of quantum electrodynamics for experiments with a ring laser,” J. Opt. Pure Appl. Opt. 2 (5), 372–379 (2000).

    Article  Google Scholar 

  21. V. I. Denisov, I. P. Denisova, and S. I. Svertilov, “Nonlinear electrodynamic delay of electromagnetic signals in a coulomb field,” Theor. Math. Phys. 135 (2), 720–726 (2003).

    Article  Google Scholar 

  22. V. I. Denisov, N. V. Kravtsov, and I. A. Krivchenkov, “A nonlinear electrodynamical shift of spectral lines in the hydrogen atom and hydrogen-like ions,” Opt. Spectrosc. 100 (5), 641–644 (2006).

    Article  Google Scholar 

  23. V. I. Denisov, N. V. Kravtsov, and I. V. Krivchenkov, “On the possibility of observing polarization of vacuum in a magnetic field,” Quant. Electron. 33 (10), 938–940 (2003).

    Article  Google Scholar 

  24. D. C. Backer, S. R. Kulkarni, C. Heiles, M. M. Davis, and W. M. Goss, “A millisecond pulsar,” Nature 300 (5893), 315–318 (1982).

    Article  Google Scholar 

  25. S. B. Popov and M. E. Prokhorov, “Progenitors with enhanced rotation and the origin of magnetars,” Mon. Not. R. Astron. Soc. 367 (2), 732–736 (2006).

    Article  Google Scholar 

  26. V. I. Denisov, I. P. Denisova, and I. V. Krivchenkov, “Path equation for photons moving in the magnetic meridian plane of a dipole magnetic field and governed by the laws of nonlinear electrodynamics in a vacuum,” Dokl. Math. 67 (1), 90–92 (2003).

    MathSciNet  MATH  Google Scholar 

  27. V. I. Denisov and S. I. Svertilov, “Vacuum nonlinear electrodynamics curvature of photon trajectories in pulsars and magnetars,” Astron. Astrophys. 399 (3), L39–L42 (2003).

    Article  Google Scholar 

  28. V. I. Denisov, I. P. Denisova, and S. I. Svertilov, “Nonlinear electrodynamic effect of ray bending in the magnetic-dipole field,” Dokl. Phys. 46 (10), 705–707 (2001).

    Article  Google Scholar 

  29. V. I. Denisov, I. V. Krivchenkov, and I. P. Denisova, “Nonlinear electrodynamic lag of electromagnetic signals in a magnetic dipole field,” J. Exp. Theor. Phys. 95 (2), 194–198 (2002).

    Article  Google Scholar 

  30. V. I. Denisov, I. P. Denisova, and S. I. Svertilov, “Nonlinear electromagnetic delay of electromagnetic signals propagating in the magnetic meridian plane of pulsars and magnetars,” Theor. Math. Phys. 140 (1), 1001–1010 (2004).

    Article  Google Scholar 

  31. V. I. Denisov, I. P. Denisova, and I. V. Krivchenkov, “Beam curvature in the magnetic field of a neutron star for an arbitrary angle between the magnetic dipole moment and incident beam,” Dokl. Phys. 48 (12), 657–659 (2003).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lomonosov Moscow State University, Leninskie Gory, Moscow, 199899, Russia

    M. G. Gapochka & A. F. Korolev

  2. Moscow State Aviation Technological University, ul. Orshanskaya 3, Moscow, 121552, Russia

    M. M. Denisov, I. P. Denisova & N. V. Kalenova

Authors
  1. M. G. Gapochka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. M. Denisov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. P. Denisova
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. N. V. Kalenova
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. F. Korolev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. G. Gapochka.

Additional information

Original Russian Text © M.G. Gapochka, M.M. Denisov, I.P. Denisova, N.V. Kalenova, A.F. Korolev, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 11, pp. 1893–1903.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gapochka, M.G., Denisov, M.M., Denisova, I.P. et al. Mathematical modeling of the nonlinear electrodynamics effect of signal delay in the magnetic field of pulsars. Comput. Math. and Math. Phys. 55, 1857–1866 (2015). https://doi.org/10.1134/S096554251511007X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S096554251511007X

Keywords

Search

Navigation