SpringerLink
Log in

The quasi-Keplerian motion in regular Bardeen spacetime

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

Abstract

We present the second post-Newtonian solution for the quasi-Keplerian motion of a test particle in the gravitational field of Bardeen black hole. This solution is formulated in terms of energy and angular momentum of the particle, as well as the black hole’s magnetic charge. The leading effects of the magnetic charge on the test particle’s orbit and motion including perihelion precession are displayed explicitly. In particular, it is shown that the magnetic charge does not have effects on the orbital period when the second post-Newtonian order is considered.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Abbott, B.P., et al.: Phys. Rev. Lett. 116, 061102 (2016)

    ADS  MathSciNet  Google Scholar 

  2. Cervantes-Cota, J.L., Galindo-Uribarri, S., Smoot, G.F.: Universe 2, 22 (2016)

    ADS  Google Scholar 

  3. Królak, A., Verma, P.: Universe 7, 137 (2021)

    ADS  Google Scholar 

  4. Akiyama, K., et al.: Astrophys. J. Lett. 875, L1 (2019)

    ADS  Google Scholar 

  5. Hawking, S.W., Penrose, R.: Proc. R. Soc. Lond. A 314, 529 (1970)

    ADS  Google Scholar 

  6. Penrose, R.: Nuovo Cimento Riv. Ser. 1, 252 (1969)

    ADS  Google Scholar 

  7. Bardeen, J.M.: Proc. GR5, Tiflis, U.S.S.R (1968)

  8. Ayón-Beato, E., García, A.: Phys. Lett. B 493, 149 (2000)

    ADS  MathSciNet  Google Scholar 

  9. Hayward, S.A.: Phys. Rev. Lett. 96, 031103 (2006)

    ADS  Google Scholar 

  10. Simpson, A., Visser, M.: JCAP 02, 042 (2019)

    ADS  Google Scholar 

  11. Ayón-Beato, E., García, A.: Phys. Rev. Lett. 80, 5056 (1998)

    ADS  Google Scholar 

  12. Eiroa, E.F., Sendra, C.M.: Class. Quantum Grav. 28, 085008 (2011)

    ADS  Google Scholar 

  13. Ghaffarnejad, H., Niad, H.: Int. J. Theor. Phys. 55, 1492 (2016)

    Google Scholar 

  14. Fernando, S., Correa, J.: Phys. Rev. D 86, 064039 (2012)

    ADS  Google Scholar 

  15. Man, J., Cheng, H.: Gen. Relativ. Gravit 46, 1559 (2014)

    Google Scholar 

  16. Bretón, N., Bergliaffa, S.E.P.: Ann. Phys. 354, 440 (2015)

    ADS  Google Scholar 

  17. Abdujabbarov, A., Amir, M., Ahmedov, B., Ghosh, S.G.: Phys. Rev. D 93, 104004 (2016)

    ADS  MathSciNet  Google Scholar 

  18. Gao, B., Deng, X.M.: Ann. Phys. 418, 168194 (2020)

    Google Scholar 

  19. Zhou, S., Chen, J., Wang, Y.: Int. J. Mod. Phys. D 21, 1250077 (2012)

    ADS  Google Scholar 

  20. Abdujabbarov, A., Ahmedov, B.: Phys. Rev. D 81, 044022 (2010)

    ADS  Google Scholar 

  21. Pugliese, D., Quevedo, H., Ruffini, R.: Phys. Rev. D 83, 024021 (2011)

    ADS  Google Scholar 

  22. Pugliese, D., Quevedo, H., Ruffini, R.: Phys. Rev. D 84, 044030 (2011)

    ADS  Google Scholar 

  23. Garcia, A., Hackmann, E., Kunz, J., Lmmerzahl, C., Macias, A.: J. Math. Phys. 56, 032501 (2015)

    ADS  MathSciNet  Google Scholar 

  24. Vrba, J., Abdujabbarov, A., Tursunov, A., Ahmedov, B., Stuchlík, Z.: Eur. Phys. J. C 79, 778 (2019)

    ADS  Google Scholar 

  25. Deng, X.M.: Phys. Dark Univer. 30, 100629 (2020)

    Google Scholar 

  26. Lin, H.Y., Deng, X.M.: Phys. Dark Univer. 31, 100745 (2021)

    Google Scholar 

  27. Gao, B., Deng, X.M.: Mod. Phys. Lett. A 36, 2150237 (2021)

    ADS  Google Scholar 

  28. Wang, Y., Sun, W., Liu, F., Wu, X.: Astrophys. J. 907, 66 (2021)

    ADS  Google Scholar 

  29. Wang, Y., Sun, W., Liu, F., Wu, X.: Astrophys. J. 909, 22 (2021)

    ADS  Google Scholar 

  30. Wu, X., Wang, Y., Sun, W., Liu, F.: Astrophys. J. 914, 63 (2021)

    ADS  Google Scholar 

  31. Brumberg, V.: Relativistic Celesctial Mechanics. Moscow in Russian, Nauka (1972)

  32. Soffel, M.H., Ruder, H., Schneider, M.: Celest. Mech. 40, 77 (1987)

    ADS  Google Scholar 

  33. Soffel, M.H.: Relativity in Astrometry. Celestial Mechanics and Geodesy. Springer, Berlin (1989)

  34. Klioner, S.A., Kopeikin, S.M.: Astrophys. J. 427, 951 (1994)

    ADS  Google Scholar 

  35. Kopeikin, S.M., Efroimsky, M., Kaplan, G.: Relativistic Celestical Mechanics of the Solar System. Wiley-VCH, New York (2012)

    MATH  Google Scholar 

  36. Damour, T., Schäfer, G.: Nuovo Cim. B 101, 127 (1988)

    ADS  Google Scholar 

  37. Schäfer, G., Wex, N.: Phys. Lett. A 174, 196 (1993)

    ADS  MathSciNet  Google Scholar 

  38. Memmesheimer, R.M., Gopakumar, A., Schäfer, G.: Phys. Rev. D 70, 104011 (2004)

    ADS  Google Scholar 

  39. Boetzel, Y., Susobhanan, A., Gopakumar, A., Klein, A., Jetzer, P.: Phys. Rev. D 96, 044011 (2017)

    ADS  MathSciNet  Google Scholar 

  40. Cho, G., Gopakumar, A., Haney, M., Lee, H.M.: Phys. Rev. D 98, 024039 (2018)

    ADS  MathSciNet  Google Scholar 

  41. Soffel, M.H., Han, W.B.: Applied General Relativity: Theory and Applications in Astronomy, Celestial Mechanics and Metrology. Springer (2019)

  42. Yang, B., Lin, W.: Gen. Relativ. Gravit. 52, 49 (2020)

    ADS  Google Scholar 

  43. Yang, B., Lin, W.: Eur. Phys. J. Plus 135, 137 (2020)

    ADS  Google Scholar 

  44. Yang, B., Jiang, C., Lin, W.: Phys. Rev. D 105, 064003 (2022)

    ADS  Google Scholar 

  45. Wex, N.: Class. Quantum Grav. 12, 983 (1995)

    ADS  MathSciNet  Google Scholar 

  46. Gergely, L.A., Perjés, Z.I., Vasúth, M.: Phys. Rev. D 57, 876 (1998)

    ADS  Google Scholar 

  47. Gergely, L.A., Perjés, Z.I., Vasúth, M.: Phys. Rev. D 57, 3423 (1998)

    ADS  Google Scholar 

  48. Gergely, L.A., Perjés, Z.I., Vasúth, M.: Phys. Rev. D 58, 124001 (1998)

    ADS  Google Scholar 

  49. Königsdörffer, C., Gopakumar, A.: Phys. Rev. D 71, 024039 (2005)

  50. Keresztes, Z., Mikóczi, B., Gergely, L.A.: Phys. Rev. D 72, 104022 (2005)

    ADS  Google Scholar 

  51. Königsdöffer, C., Gopakumar, A.: Phys. Rev. D 73, 044011 (2006)

  52. Gopakumar, A., Schäfer, G.: Phys. Rev. D 84, 124007 (2011)

    ADS  Google Scholar 

  53. Bohé, A., Marsat, S., Faye, G., Blanchet, L.: Class. Quantum Grav. 30, 075017 (2013)

    ADS  Google Scholar 

  54. Gergely, L.A., Keresztes, Z.: Phys. Rev. D 91, 024012 (2015)

    ADS  Google Scholar 

  55. Mikóczi, B.: Phys. Rev. D 95, 064023 (2017)

    ADS  MathSciNet  Google Scholar 

  56. Yang, B., Lin, W.: Phys. Scr. 95, 105008 (2020)

    ADS  Google Scholar 

  57. Yang, B., Lin, W.: Phys. Scr. 96, 085007 (2021)

    ADS  Google Scholar 

  58. Tessmer, M., Hartung, J., Schäfer, G.: Class. Quantum Grav. 27, 165005 (2010)

    ADS  Google Scholar 

  59. Laurentis, M.D., Rosa, R.D., Garufi, F., Milano, L.: Mon. Not. R. Astron. Soc. 424, 2371 (2012)

    ADS  Google Scholar 

  60. Martino, I.D., Lazkoz, R., Laurentis, M.D.: Phys. Rev. D 97, 104067 (2018)

    ADS  MathSciNet  Google Scholar 

  61. Laurentis, M.D., Martino, I.D., Lazkoz, R.: Eur. Phys. J. C 78, 916 (2018)

    ADS  Google Scholar 

  62. Laurentis, M.D., Martino, I.D., Lazkoz, R.: Phys. Rev. D 97, 104068 (2018)

    ADS  MathSciNet  Google Scholar 

  63. Abuter, R., Amorim, A., Bauböck, M., et al.: Astron. Astrophys. 636, L5 (2020)

    ADS  Google Scholar 

  64. Zhou, T.Y., **e, Y.: Eur. Phys. J. C 80, 1070 (2020)

    ADS  Google Scholar 

  65. Zhang, J., **e, Y.: Eur. Phys. J. C 82, 854 (2022)

    ADS  Google Scholar 

  66. Zhang, J., **e, Y.: Astrophys. Space Sci. 367, 17 (2022)

    ADS  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Prof. Remo Ruffini for helpful discussions. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 12247157, 12303079 and 11973025), and Scientific Research Fund of Hunan Provincial Education Department (Grant No. 22B0446). Thanks in part for the support of the postdoctoral program of purple Mountain Observatory, Chinese Academy of Sciences.

Author information

Authors and Affiliations

  1. School of Mathematics and Physics, University of South China, Hengyang, 421001, China

    Jie Li, Bo Yang & Wenbin Lin

  2. Purple Mountain Observatory, Chinese Academy of Sciences, Nan**g, 210023, China

    Bo Yang

  3. ICRA-Dip. di Fisica, University of Rome, P.le Aldo Moro, 5, 00185, Rome, Italy

    Yu Wang

  4. INAF-Osservatorio Astronomico d’Abruzzo, Via M. Maggini snc, 64100, Teramo, Italy

    Yu Wang

Authors
  1. Jie Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bo Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wenbin Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J. Li and B. Yang did the calculations. Y. Wang and W. Lin checked the calculation results. All authors participated in writing the manuscript text. The revisions were mainly done by B. Yang.

Corresponding author

Correspondence to Bo Yang.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, J., Yang, B., Wang, Y. et al. The quasi-Keplerian motion in regular Bardeen spacetime. Gen Relativ Gravit 55, 114 (2023). https://doi.org/10.1007/s10714-023-03166-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-023-03166-9

Keywords

Search

Navigation