Skip to main content
SpringerLink
Log in

Shadows of rotating quintessential black holes in Einstein–Gauss–Bonnet gravity with a cloud of strings

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

Abstract

Using the Newman–Janis algorithm, we study certain optical behaviors of rotating quintessential black holes in Einstein Gauss–Bonnet gravity models with a cloud of strings. Concretely, we investigate the shadow behaviors in terms of one dimensional real curves. By elaborating the associated null geodesic equations of motion, we illustrate the shadow geometries in terms of an appropriate moduli space involving external dark field contributions. Among others, we find that the string cloud parameter serves as a geometric quantity controlling the shadow size. We approach graphically the corresponding astronomical observables. Then, we compute and analyze the energy emission rate by varying the involved parameters. Finally, we discuss a possible connection with observations from Event Horizon Telescope by providing certain constraints on the involved black hole parameters in the light of the \(\hbox {M}87^*\) image.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Cvetic, M., et al.: Embedding AdS black holes in ten and eleven dimensions. Nucl. Phys. B 558, 96 (1999). arXiv:hep-th/9903214

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Hawking, S.W., Page, D.N.: Thermodynamics of black holes in anti-de Sitter space. Commun. Math. Phys. 87(4), 577 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  3. Belhaj, A., Chabab, M., El Moumni, H., Sedra, M.B.: On thermodynamics of AdS black holes in arbitrary dimensions. CPL 29, 100401 (2012). arXiv:1210.4617

    Google Scholar 

  4. Liu, Y., Zou, D.C., Wang, B.: Signature of the Van der Waals like small-large charged AdS black hole phase transition in quasi normal modes. JHEP 09, 179 (2014). arXiv:1405.2644

    Article  ADS  MATH  Google Scholar 

  5. Belhaj, A., El Balali, A., El Hadri, W., Torrente-Lujan, E.: On universal constants of AdS black holes from Hawking–Page phase transition. Phys. Lett. B 811, 135871 (2020). arXiv:2010.07837

    Article  MathSciNet  MATH  Google Scholar 

  6. Rajagopal, A., Kubiznak, D., Mann, R.B.: Van der Waals black hole. Phys. Lett. B 737, 277 (2014). arXiv:1408.1105

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Herscovich, E., Richarte, M.G.: Black holes in Einstein–Gauss–Bonnet gravity with a string cloud background. Phys. Lett. B 689, 192 (2010). arXiv: 1004.3754

    Article  ADS  MathSciNet  Google Scholar 

  8. Toledo, J.M., Bezerra, V.B.: Some remarks on the thermodynamics of charged AdS black holes with cloud of strings and quintessence. Eur. Phys. J. C 79, 110 (2019)

    Article  ADS  Google Scholar 

  9. Chabab, M., Iraoui, S.: Thermodynamic criticality of d-dimensional charged AdS black holes surrounded by quintessence with a cloud of strings background. Gen. Relativ. Gravit. 52, 53 (2020). arXiv:2001.06063

    Article  MathSciNet  MATH  Google Scholar 

  10. Abbott, B., et al.: Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116(6), 061102 (2016). arXiv:1602.03837

    Article  ADS  MathSciNet  Google Scholar 

  11. Akiyama, K., et al.: First M87 event horizon telescope results. IV. Imaging the central supermassive black hole. Astrophys. J. L4(1), 875 (2019). arXiv:1906.11241

    Google Scholar 

  12. Akiyama, K., et al.: First M87 event horizon telescope results. V. Imaging the central supermassive black hole. Astrophys. J. L5(1), 875 (2019)

    Google Scholar 

  13. Akiyama, K., et al.: First M87 event horizon telescope results. VI. Imaging the central supermassive black hole. Astrophys. J. L6(1), 875 (2019)

    Google Scholar 

  14. Wei, S.W., Zou, Y.C., Liu, Y.X., Mann, R.B.: Curvature radius and Kerr black hole shadow. JCAP 08, 030 (2019). arXiv:1904.07710

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Övgün, A., Sakalli, I., Saavedra, J.: Shadow cast and Deflection angle of Kerr–Newman–Kasuya spacetime. JCAP 10, 041 (2018). arXiv:1807.00388

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Belhaj, A., Belmahi, H., Benali, M., El Hadri, W., El Moumni, H., Torrente-Lujan, E.: Shadows of 5D Black Holes from string theory. Phys. Lett. B 812, 136025 (2021). arXiv:2008.13478

    Article  MathSciNet  MATH  Google Scholar 

  17. Belhaj, A., Benali, M., El Balali, A., El Hadri, W., El Moumni, H., Torrente-Lujan, E.: Black hole shadows in M-theory scenarios. Int. J. Mod. Phys. D 30, 2150026 (2021). arXiv:2008.09908

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Konoplya, R.: Shadow of a black hole surrounded by dark matter. Phys. Lett. B 795, 1 (2019). arXiv:1905.00064

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Khan, S.U., Ren, J.: Shadow cast by a rotating charged black hole in quintessential dark energy. Phys. Dark Univ. 30, 100644 (2020). arXiv:2006.11289

    Article  Google Scholar 

  20. Hou, X., Xu, Z., Wang, J.: Rotating black hole shadow in perfect fluid dark matter. JCAP 12, 040 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Belhaj, A., Benali, M., El Balali, A., El Moumni, H., Ennadifi, S.-E.: Deflection angle and shadow behaviors of quintessential black holes in arbitrary dimensions. Class. Quantum Grav. 37, 215004 (2020). arXiv:2006.01078

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Lovelock, D.: The Einstein tensor and its generalizations. J. Math. Phys. 12, 498 (1971). arXiv:gr-qc/9510060

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Boulware, D.G., Deser, S.: String-generated gravity models. Phys. Rev. Lett. 55, 2656 (1985)

    Article  ADS  Google Scholar 

  24. Wheeler, J.T.: Symmetric solutions to the Gauss–Bonnet extended Einstein equations. Nucl. Phys. B 268, 737 (1986)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Glavan, D., Lin, C.: Einstein–Gauss–Bonnet gravity in 4-dimensional space-time. Phys. Rev. Lett. 124, 081301 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  26. Ghosh, S.G., Kumar, R.: Generating black holes in 4D Einstein–Gauss–Bonnet gravity. Class. Quant. Grav. 37, 245008 (2020). arXiv:2003.12291

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Ghosh, S.G., Maharaj, S.D.: Radiating black holes in the novel 4D Einstein–Gauss–Bonnet gravity. Phys. Dark Univ. 30, 100687 (2020). arXiv:2003.09841

    Article  Google Scholar 

  28. Singh, D.V., Kumar, R., Ghosh, S.G., Maharaj, S.D.: Phase transition of AdS black holes in 4D EGB gravity coupled to nonlinear electrodynamics. Ann. Phys. 424, 168347 (2021). arXiv:2006.00594

    Article  MathSciNet  MATH  Google Scholar 

  29. Wei, S.W., Liu, Y.X.: Extended thermodynamics and microstructures of four-dimensional charged Gauss–Bonnet black hole in AdS space. Phys. Rev. D 101, 104018 (2020). arXiv: 2003.14275

    Article  ADS  MathSciNet  Google Scholar 

  30. Heydari-Fard, M., Heydari-Fard, M.: Null geodesics and shadow of 4D Einstein–Gauss–Bonnet black holes surrounded by quintessence. arXiv: 2109.02059

  31. Kiselev, V.V.: Quintessence and black holes. Class. Quant. Grav. 20, 1187 (2003). arXiv:gr-qc/0210040

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Chen, S., Wang, B., Su, R.: Hawking radiation in a d-dimensional static spherically symmetric black hole surrounded by quintessence. Phys. Rev. D 77, 124011 (2008). arXiv:0801.2053

    Article  ADS  MathSciNet  Google Scholar 

  33. Letelier, P.S.: Clouds of strings in general relativity. Phys. Rev. D 20, 1294 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  34. Myers, R.C., Simon, J.Z.: Black-hole thermodynamics in Lovelock gravity. Phys. Rev. D 38, 2434 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  35. Shah, H., Ahmad, Z., Shah, H.H.: Quintessence background for 4D Einstein–Gauss–Bonnet black holes. Phys. Lett. B 818, 136383 (2021). arXiv:2003.12291

    Article  MATH  Google Scholar 

  36. Singh, D.V., Ghosh, S.G., Maharaj, S.D.: Clouds of strings in 4D Einstein–Gauss–Bonnet black holes. Phys. Dark Univ. 30, 100730 (2020)

    Article  Google Scholar 

  37. Newman, E., Janis, A.: Note on the Kerr spinning-particle metric. J. Math. Phys. 6, 915 (1965)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Carter, B.: Global structure of the Kerr family of gravitational fields. Phys. Rev. 174, 1559 (1968)

    Article  ADS  MATH  Google Scholar 

  39. Kumar, R., Ghosh, S.G.: Rotating black holes in 4D Einstein–Gauss–Bonnet gravity and its shadow. J. Cosmol. Astropart. Phys 07, 053 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  40. Vazquez, A.E., Esteban, E.P.: Strong field gravitational lensing by a Kerr Black Hole. Nuovo Cim. B 119, 489 (2004)

    ADS  MathSciNet  Google Scholar 

  41. Liddle, A.R., Lyth, D.H.: Cosmological Inflation and Large-Scale Structure. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  42. Belhaj, A., El Balali, A., El Hadri, W., Essebani, M.A., Sedra, M.B., Segui, A.: Kerr-AdS black hole behaviors from dark energy. Int. J. Mod. Phys. D 29(09), 2050069 (2020)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. Hioki, K., Maeda, K.I.: Measurement of the Kerr spin parameter by observation of a compact object’s shadow. Phys. Rev. D 80, 024042 (2009)

    Article  ADS  Google Scholar 

  44. Amir, M., Ghosh, S.G.: Shapes of rotating nonsingular black hole shadows. Phys. Rev. D 94, 024054 (2016). arXiv:1603.06382

    Article  ADS  MathSciNet  Google Scholar 

  45. Wei, S.W., Liu, Y.X.: Observing the shadow of Einstein–Maxwell–Dilaton–Axion black hole. JCAP 11, 063 (2013). arXiv:1311.4251

    Article  ADS  Google Scholar 

  46. Khodadi, M., Allahyari, A., Vagnozzi, S., Mota, D.F.: Black holes with scalar hair in light of the event horizon telescope. arXiv:2005.05992

  47. Khodadi, M., Saridakis, E.N.: Einstein–Æther gravity in the light of event horizon telescope observations of M87\(^*\). Phys. Dark Univ. 32, 100835 (2021). arXiv:2012.05186

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank H. Belmahi and M. Benali for discussions, scientific help, and correspondence on this project work. They would like also to thank the anonymous referee for interesting comments and suggestions.

Author information

Authors and Affiliations

  1. Département de Physique, Équipe des Sciences de la matière et du Rayonnement, ESMaR, Faculté des Sciences, Université Mohammed V de Rabat, Rabat, Morocco

    Adil Belhaj & Yassine Sekhmani

Authors
  1. Adil Belhaj
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yassine Sekhmani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adil Belhaj.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Belhaj, A., Sekhmani, Y. Shadows of rotating quintessential black holes in Einstein–Gauss–Bonnet gravity with a cloud of strings. Gen Relativ Gravit 54, 17 (2022). https://doi.org/10.1007/s10714-022-02902-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-022-02902-x

Keywords

Search

Navigation