Skip to main content
SpringerLink
Log in

The \(SO(3,1) \times U(1)\)-gauge invariant approach to charged bosons in relativistic magnetars

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

Abstract

Using a perturbative method, we investigate solutions of the Klein–Gordon equations for a charged massive field in the background of a magnetar, both in the interior solution and outside the star. A special attention is given to cases where the variables can be separated and the wave function is expressed in terms of the Heun’s general or confluent functions. By imposing various conditions on the parameters, one gets the energy quantization law and simple polynomial forms of the Heun’s functions, which can be used in computing first-order transition amplitudes.

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

Notes

  1. This basically sets the non-vanishing component of the electromagnetic potential to be directed along the \(\varphi \)-direction [19].

  2. Note that in Yazadjiev’s solution the stress-energy tensor of the fluid has only diagonal components.

References

  1. Duncan, R., Thompson, C.: ApJ 392, L9 (1992)

    Article  ADS  Google Scholar 

  2. Olausen, S.A., Kaspi, V.M.: Astrophys. J. Suppl. 212, 6 (2014). https://doi.org/10.1088/0067-0049/212/1/6. arXiv:1406.7230 [astro-ph.HE]

    Article  ADS  Google Scholar 

  3. Ciolfi, R.: Astron. Nachr. 335, 624 (2014). https://doi.org/10.1002/asna.201412083. arXiv:1703.00068 [astro-ph.HE]

    Article  ADS  Google Scholar 

  4. Kaspi, V.M., Beloborodov, A.: arXiv:1703.00068 [astro-ph.HE]

  5. Mereghetti, S.: Astron. Astrophys. Rev. 15, 225 (2008). https://doi.org/10.1007/s00159-008-0011-z. arXiv:0804.0250 [astro-ph]

    Article  ADS  Google Scholar 

  6. Turolla, R., Zane, S., Watts, A.: Rep. Prog. Phys. 78(11), 116901 (2015). https://doi.org/10.1088/0034-4885/78/11/116901. arXiv:1507.02924 [astro-ph.HE]

    Article  ADS  Google Scholar 

  7. Boquet, M., Bonazzola, S., Novak, J.: Astron. Astrophys. 301, 757 (1995)

    ADS  Google Scholar 

  8. Cardall, C.Y., Prakash, M., Lattimer, L.M.: ApJ 554, 322 (2001)

    Article  ADS  Google Scholar 

  9. Kiuchi, K., Yoshida, S.: Phys. Rev. D 78, 044045 (2008). https://doi.org/10.1103/PhysRevD.78.044045. arXiv:0802.2983 [astro-ph]

    Article  ADS  Google Scholar 

  10. Ciolfi, R., Ferrari, V., Gualtieri, L., Pons, J.A.: Mon. Not. Rroyal. Astron. Soc. 397, 913 (2009). https://doi.org/10.1111/j.1365-2966.2009.14990.x. arXiv:0903.0556 [astro-ph.SR]

    Article  ADS  Google Scholar 

  11. Yazadjiev, S.: Phys. Rev. D 85, 044030 (2012). https://doi.org/10.1103/PhysRevD.85.044030. arXiv:1111.3536 [gr-qc]

    Article  ADS  Google Scholar 

  12. Duncan, R., Thompson, C.: ApJ 473, 322 (1996)

    Article  ADS  Google Scholar 

  13. Heun, K.: Math. Ann. 33, 161 (1889)

    Article  Google Scholar 

  14. Ronveaux, A. (ed.): Heuns Differential Equations. Oxford University Press, New York (1995)

    Google Scholar 

  15. Slavyanov, S.Y., Lay, W.: Special Functions, A Unified Theory Based on Singularities, Oxford Mathematical Monographs, Oxford University Press (2000)

  16. Al-Badawi, A.: arXiv:1702.01380 [gr-qc]

  17. Birkandan, T., Hortasu, M.: arXiv:1704.00294 [math-ph]

  18. Passamonti, A., Pons, J.A.: Mon. Not. R. Astron. Soc. 463(2), 1173 (2016). https://doi.org/10.1093/mnras/stw1880. arXiv:1606.02132 [astro-ph.HE]

    Article  ADS  Google Scholar 

  19. Colaiuda, A., Ferrari, V., Gualtieri, L., Pons, J.A.: Mon. Not. R. Astron. Soc. 385, 2080 (2008). https://doi.org/10.1111/j.1365-2966.2008.12966.x. arXiv:0712.2162 [astro-ph]

    Article  ADS  Google Scholar 

  20. Hernandez-Pastora, J.L., Herrera, L., Martin, J.: Class. Quant. Gravit. 33(23), 235005 (2016). https://doi.org/10.1088/0264-9381/33/23/235005. arXiv:1607.02315 [gr-qc]

    Article  ADS  Google Scholar 

  21. Herrera, L., Di Prisco, A., Ibez, J., Ospino, J.: Phys. Rev. D 87(2), 024014 (2013). https://doi.org/10.1103/PhysRevD.87.024014. arXiv:1301.2424 [gr-qc]

    Article  ADS  Google Scholar 

  22. Heinicke, C., Hehl, F.W.: Int. J. Mod. Phys. D 24(02), 1530006 (2014). https://doi.org/10.1142/S0218271815300062. arXiv:1503.02172 [gr-qc]

    Article  ADS  Google Scholar 

  23. Maple 2016. Maplesoft, a division of Waterloo Maple Inc., Waterloo, Ontario

  24. da Silva Leite, L.G., Filgueiras, C., Cogollo, D., Silva, E.O.: Phys. Lett. A 379, 907 (2015)

    Article  Google Scholar 

  25. Buchdahl, H.A.: General relativistic uid spheres. Phys. Rev. 116, 10271034 (1959)

    Article  Google Scholar 

  26. Vieira, H.S., Bezerra, V.B.: Ann. Phys. 373, 28 (2016). https://doi.org/10.1016/j.aop.2016.06.016. arXiv:1603.02233 [gr-qc]

    Article  ADS  Google Scholar 

  27. Yumisaki, H.: PTEP 2017, no. 6, 063B04 (2017) https://doi.org/10.1093/ptep/ptx075 [arXiv:1606.09626 [gr-qc]]

Download references

Acknowledgements

This work was financially supported by UEFISCDI through the PN-III-P4-ID-PCE-2016-0131 program.

Author information

Authors and Affiliations

  1. Faculty of Physics, “Alexandru Ioan Cuza” University, 11 Bd. Carol I, 700506, Iasi, Romania

    Ciprian Dariescu & Marina-Aura Dariescu

  2. Research Department, Faculty of Physics, “Alexandru Ioan Cuza” University, 11 Bd. Carol I, 700506, Iasi, Romania

    Cristian Stelea

Authors
  1. Ciprian Dariescu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marina-Aura Dariescu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cristian Stelea
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cristian Stelea.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dariescu, C., Dariescu, MA. & Stelea, C. The \(SO(3,1) \times U(1)\)-gauge invariant approach to charged bosons in relativistic magnetars. Gen Relativ Gravit 49, 153 (2017). https://doi.org/10.1007/s10714-017-2314-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-017-2314-8

Keywords

Search

Navigation