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Shadows and quasinormal modes of the Bardeen black hole in cloud of strings

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Abstract

We investigate the black hole solution of Einstein’s gravity coupled with non-linear electrodynamics (NED) source in the background of a cloud of strings. We analyze the horizon structure and optical features of the black hole. The photon radius and shadows are obtained as a function of black hole parameters. We observe that the size of the shadow image is bigger than its horizon radius and photon sphere. We also study the quasi-normal modes using WKB formula for this black hole. The dependence of shadow radius and quasi-normal modes on black hole parameters reflects that they are mimicker to each other.

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Data sharing is not applicable to this article as no data sets were generated or analyzed during the current study.

References

  1. E.S. Fradkin, A.A. Tseytlin, Phys. Lett. B 163, 123 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  2. R. Penrose, Phys. Rev. Lett. 14, 57 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  3. S.W. Hawking, Proc. R. Soc. Lond. A 300, 187 (1967)

    Article  ADS  Google Scholar 

  4. S.W. Hawking, R. Penrose, Proc. R. Soc. Lond. A 3(14), 529 (1970)

    ADS  Google Scholar 

  5. J. Bardeen, Proceedings of GR5 (Tiflis, U.S.S.R., 1968)

  6. K. Jafarzade, M. Kord Zangeneh, F.S.N. Lobo, JCAP 04, 008 (2021)

    Article  ADS  Google Scholar 

  7. D.V. Singh, A. Shukla, S. Upadhyay, Ann. Phys. 447, 169157 (2022)

    Article  Google Scholar 

  8. D.V. Singh, V.K. Bhardwaj, S. Upadhyay, Eur. Phys. J. Plus 137(8), 969 (2022)

    Article  Google Scholar 

  9. A. Belhaj, L. Chakhchi, H. El Moumni, J. Khalloufi, K. Masmar, Int. J. Mod. Phys. A 35(27), 2050170 (2020)

    Article  ADS  Google Scholar 

  10. B. Eslam Panah, K. Jafarzade, S.H. Hendi, Nucl. Phys. B 961, 269115 (2020)

    Article  Google Scholar 

  11. E. Ayon-Beato, A. Garcia, Gen. Rel. Grav. 31, 629 (1999)

    Article  ADS  Google Scholar 

  12. E. Ayon-Beato, A. Garcia, Phys. Lett. B 493, 149 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  13. S. Fernando, Int. J. Mod. Phys. D 26, 1750071 (2017)

    Article  ADS  Google Scholar 

  14. D.V. Singh, N.K. Singh, Ann. Phys. 383, 600–609 (2017)

    Article  ADS  Google Scholar 

  15. C. Bambi, L. Modesto, Phys. Lett. B 721, 329 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  16. F. Ahmed, D.V. Singh, S.G. Ghosh, Gen. Rel. Grav. 54(2), 21 (2022)

    Article  ADS  Google Scholar 

  17. M. Sharif, W. Javed, Can. J. Phys. 89, 1027 (2011)

    Article  ADS  Google Scholar 

  18. D.V. Singh, M.S. Ali, S.G. Ghosh, Int. J. Mod. Phys. D 27(12), 1850108 (2018)

    Article  ADS  Google Scholar 

  19. T.G. Rizzo, JHEP 09, 021 (2006)

    Article  ADS  Google Scholar 

  20. S.G. Ghosh, A. Kumar, D.V. Singh, Phys. Dark Univ. 30, 100660 (2020)

    Article  Google Scholar 

  21. S.G. Ghosh, D.V. Singh, R. Kumar, S.D. Maharaj, Ann. Phys. 424, 168347 (2021)

    Article  Google Scholar 

  22. D.V. Singh, S.G. Ghosh, S.D. Maharaj, Phys. Dark Univ. 30, 100730 (2020)

    Article  Google Scholar 

  23. D.V. Singh, S.G. Ghosh, S.D. Maharaj, Ann. Phys. 412, 168025 (2020)

    Article  Google Scholar 

  24. B.K. Singh, R.P. Singh, D.V. Singh, Eur. Phys. J. Plus 13510, 862 (2020)

    Article  Google Scholar 

  25. B.K. Singh, R.P. Singh, D.V. Singh, Eur. Phys. J. Plus 136(5), 575 (2021)

    Article  Google Scholar 

  26. R.V. Maluf, J.C.S. Neves, Phys. Rev. D 97, 104015 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  27. Mang-Sen. Ma, Ren Zhao, Class. Quantun Grav. 31, 245014 (2014)

    Article  ADS  Google Scholar 

  28. D.V. Singh, S.G. Ghosh, S.D. Maharaj, Ann. Phys. 412, 168025 (2020)

    Article  Google Scholar 

  29. Md. Sabir Ali, S.G. Ghosh, Phys. Rev. D 98, 084025 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  30. K.A. Bronnikov, Phys. Rev. D 63, 044005 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  31. A. Simpson, M. Visser, arXiv:1911.01020 [gr-qc]

  32. A. Simpson, M. Visser, arXiv:1911.01020 [gr-qc]

  33. D.V. Singh, S.G. Ghosh, S.D. Maharaj, Nucl. Phys. B 981, 115854 (2022)

    Article  Google Scholar 

  34. D.V. Singh, S. Siwach, Phys. Lett. B 808, 135658 (2020)

    Article  MathSciNet  Google Scholar 

  35. B. Singh, B.K. Singh, D.V. Singh, Int. J. Geom. Meth. Mod. Phys. 20(08), 23501 (2023)

    Article  Google Scholar 

  36. M.E. Rodrigues, H.A. Vieira, Phys. Rev. D 1068, 084015 (2022)

    Article  ADS  Google Scholar 

  37. M.E. Rodrigues, M..Vd.S. Silva, Phys. Rev. D 106(8), 084016 (2022)

    Article  ADS  Google Scholar 

  38. C.M. Claudel, K.S. Virbhadra, G.F.R. Ellis, J. Math. Phys. 42, 818–838 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  39. N. Tsukamoto, Z. Li, C. Bambi, JCAP 06, 043 (2014)

    Article  ADS  Google Scholar 

  40. P.C. Li, T.C. Lee, M. Guo, B. Chen, Phys. Rev. D 104(8), 084044 (2021)

    Article  ADS  Google Scholar 

  41. B. Cuadros-Melgar, R.D.B. Fontana, J. de Oliveira, Phys. Lett. B 811, 135966 (2020)

    Article  MathSciNet  Google Scholar 

  42. Filipe Moura, João. Rodrigues, Phys. Lett. B 819, 136407 (2021)

    Article  Google Scholar 

  43. A.D. Sakharov, Sov. Phys. JETP 22, 241 (1966)

    ADS  Google Scholar 

  44. E.B. Gliner, Sov. Phys. JETP 22, 378 (1966)

    ADS  Google Scholar 

  45. K. Akiyama et al., Astrophys. J. 875, L1 (2019)

    Article  ADS  Google Scholar 

  46. K. Akiyama et al., Astrophys. J. 875, L4 (2019)

    Article  ADS  Google Scholar 

  47. S. Vagnozzi et al., arXiv:2205.07787 [gr-qc]

  48. P.S. Letelier, Phys. Rev. D 28, 2414 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  49. P.S. Letelier, Phys. Rev. D 20, 1294 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  50. P.S. Letelier, Il Nuovo Cim. B 63, 519 (1981)

    Article  ADS  Google Scholar 

  51. J.L. Synge, Relativity: The General Theory (North Holland, Amsterdam, 1966), p.175

    Google Scholar 

  52. A. Belhaj, H. Belmahi, M. Benali, W. El Hadri, H. El Moumni, E. Torrente-Lujan, Phys. Lett. B 812, 136025 (2021)

    Article  Google Scholar 

  53. A. Belhaj, Y. Sekhmani, Gen. Rel. Grav. 54(2), 17 (2022)

    Article  ADS  Google Scholar 

  54. A. Belhaj, H. Belmahi, M. Benali, A. Segui, Phys. Lett. B 817, 136313 (2021)

    Article  Google Scholar 

  55. V. Perlick, O.Y. Tsupko, G.S. Bisnovatyi-Kogan, Phys. Rev. D 92(10), 104031 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  56. B.F. Schutz, C.M. Will, Astrophys J. 291, L33 (1985)

    Article  ADS  Google Scholar 

  57. S. Iyer, C.M. Will, Phys. Rev. D 35, 3621 (1987)

    Article  ADS  Google Scholar 

  58. R.A. Konoplya, Phys. Rev. D 68, 024018 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  59. Y. Myrzakulov, K. Myrzakulov, S. Upadhyay, D.V. Singh, Int. J. Geom. Meth. Mod. Phys. 20, 2350121 (2023)

    Article  Google Scholar 

  60. V. Cardoso, A.S. Miranda, E. Berti, H. Witek, V.T. Zanchin, Phys. Rev. D 79, 064016 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  61. R.A. Konoplya, Z. Stuchlík, Phys. Lett. B 771, 597–602 (2017)

    Article  ADS  Google Scholar 

  62. R.A. Konoplya, Phys. Lett. B 838, 137674 (2023)

    Article  Google Scholar 

Download references

Acknowledgements

The work of BKV is supported by UGC fellowship. DVS thanks to the DST-SERB project (Grant No. EEQ/2022/000824).

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Correspondence to Sanjay Siwach.

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Vishvakarma, B.K., Singh, D.V. & Siwach, S. Shadows and quasinormal modes of the Bardeen black hole in cloud of strings. Eur. Phys. J. Plus 138, 536 (2023). https://doi.org/10.1140/epjp/s13360-023-04174-z

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