Skip to main content
SpringerLink
Log in

Black holes in 4D AdS Einstein Gauss Bonnet gravity with power: Yang Mills field

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

Abstract

In this paper we construct an exact spherically symmetric black hole solution with a power Yang–Mills (YM) source in the context of 4D Einstein Gauss–Bonnet gravity (4D EGB). We choose our source as \((F_{\mu \nu }^{(a)}F^{\mu \nu (a)})^q\), where q is an arbitrary positive real number. Thereafter we study the horizon structure, thermodynamic issues like thermal stability and black hole phase transition. Our purpose here is to analyse the black hole space-time under the net effect coming from the Gauss–Bonnet coupling parameter \(\alpha \) and the nonlinear parameter q. We then evaluate all important thermodynamic quantities to establish the Smarr formula and the first law of thermodynamics in extended phase space. The behaviour of heat capacity as a function of horizon radius is thoroughly studied to understand the thermal stability of the black hole solution. An interesting phenomena of existence/absence of thermal phase transition occur due to the nonlinearity of YM source. For some values of the parameters, we find that the solution exhibits a first-order phase transition, like a van der Waals fluid. In addition, we also verify Maxwell’s equal area law numerically by crucial analysis of Gibbs free energy as a function of temperature. Moreover, the critical exponents are derived and showed the universality class of the scaling behaviour of thermodynamic quantities near criticality.

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

Data availability

All data generated or analysed during this study are included in this article.

Notes

  1. See recent review [13] and references therein for related phenomena of phase transition of black hole systems.

  2. Where \(F_{\mu \nu }^{(a)}\) is the YM field with its internal index \(1 \le a \le \frac{1}{2}(D-2)(D-1).\)

References

  1. Hawking, S.W.: Nature 248, 30 (1974)

    Article  ADS  Google Scholar 

  2. Hawking, S.W.: Commun. Math. Phys. 43, 199 (1975)

    Article  ADS  Google Scholar 

  3. Bekenstein, J.D.: Phys. Rev. D 7, 2333 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  4. Hawking, S., Page, D.N.: Commun. Math. Phys. 87, 577 (1983)

    Article  ADS  Google Scholar 

  5. Maldacena, J.M.: Int. J. Theor. Phys. 38, 1113 (1999). [hep-th/9711200]

    Article  Google Scholar 

  6. Witten, E.: Adv. Theor. Math. Phys. 2, 253 (1998). [hep-th/9802150]

    Article  ADS  MathSciNet  Google Scholar 

  7. Witten, E.: Adv. Theor. Math. Phys. 2, 505 (1998). [hep-th/9803131]

    Article  MathSciNet  Google Scholar 

  8. Chamblin, A., Emparan, R., Johnson, C., Myers, R.: Phys. Rev. D 60, 064018 (1999). [hep-th/9902170]

    Article  ADS  MathSciNet  Google Scholar 

  9. Chamblin, A., Emparan, R., Johnson, C., Myers, R.: Phys. Rev. D 60, 104026 (1999). [hep-th/9904197]

    Article  ADS  MathSciNet  Google Scholar 

  10. Kastor, D., Ray, S., Traschen, J.: Class. Quantum Grav. 26, 195011 (2009). arXiv:0904.2765

    Article  ADS  Google Scholar 

  11. Dolan, B.: Class. Quantum Grav. 28, 125020 (2011). arXiv:1008.5023

    Article  ADS  Google Scholar 

  12. Kubiznak, D., Mann, R.B.: JHEP 1207, 033 (2012). arXiv:1205.0559

    Article  ADS  Google Scholar 

  13. Kubiznak, D., Mann, R.B., Teo, M.: Class. Quantum Grav. 34, 063001 (2017). arXiv:1608.06147 [hep-th]

    Article  ADS  Google Scholar 

  14. Berti, E., et al.: Class. Quantum Grav. 32, 243001 (2015). arXiv:1501.07274 [gr-qc]

    Article  ADS  Google Scholar 

  15. Barack, L., et al.: Class. Quantum Grav. 36, 143001 (2019). arXiv:1806.05195 [gr-qc]

    Article  ADS  Google Scholar 

  16. Gross, D.J., Witten, E.: Nucl. Phys. B 277, 1 (1986)

    Article  ADS  Google Scholar 

  17. Gross, D.J., Sloan, J.H.: Nucl. Phys. B 291, 41 (1987)

    Article  ADS  Google Scholar 

  18. Metsaev, R.R., Tseytlin, A.A.: Phys. Lett. B 191, 354 (1987)

    Article  ADS  Google Scholar 

  19. Zwiebach, B.: Phys. Lett. B 156, 315 (1985)

    Article  ADS  Google Scholar 

  20. Metsaev, R.R., Tseytlin, A.A.: Nucl. Phys. B 293, 385 (1987)

    Article  ADS  Google Scholar 

  21. Lovelock, D.: J. Math. Phys. 12, 498 (1971)

    Article  ADS  Google Scholar 

  22. Lovelock, D.: J. Math. Phys. 13, 874 (1972)

    Article  ADS  Google Scholar 

  23. Glavan, D., Lin, C.: Phys. Rev. Lett. 124, 081301 (2020). arXiv:1905.03601 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  24. Gurses, M., Sisman, T.C., Tekin, B.: Phys. Rev. Lett. 125, 149001 (2020). arXiv:2009.13508 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  25. Gurses, M., Sisman, T.C., Tekin, B.: Eur. Phys. J. C 80, 647 (2020)

    Article  ADS  Google Scholar 

  26. Mahapatra, S.: Eur. Phys. J. C 80, 992 (2020)

    Article  ADS  Google Scholar 

  27. Kobayashi, T.: JCAP 7, 013 (2020)

    Article  ADS  Google Scholar 

  28. Bonifacio, J., Hinterbichler, K., Johnson, L.A.: Phys. Rev. D 102, 024029 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  29. Arrechea, J., Delhom, A., Jiménez-Cano, A.: Chin. Phys. C 45, 013107 (2021)

    Article  ADS  Google Scholar 

  30. Hohmann, M., Pfeifer, C., Voicu, N.: Eur. Phys. J. Plus 136, 180 (2021)

    Article  Google Scholar 

  31. Hennigar, R.A., Kubiznak, D., Mann, R.B., Pollack, C.: JHEP 07, 027 (2020). arXiv:2004.09472

    Article  ADS  Google Scholar 

  32. Casalino, A., Colleaux, A., Rinaldi, M., Vicentini, S.: Phys. Dark Univ. 31, 100770 (2021). arXiv:2003.07068 [gr-qc]

    Article  Google Scholar 

  33. Lu, H., Pang, Y.: Phys. Lett. B 809, 135717 (2020). arXiv:2003.11552

    Article  MathSciNet  Google Scholar 

  34. Bonifacio, J., Hinterbichler, K., Johnson, L.A.: Phys. Rev. D 102, 024029 (2020). arXiv:2004.10716

    Article  ADS  MathSciNet  Google Scholar 

  35. Fernandes, P.G.S., Carrilho, P., Clifton, T., Mulryne, D.J.: Phys. Rev. D 102, 024025 (2020). arXiv:2004.08362

    Article  ADS  MathSciNet  Google Scholar 

  36. Kobayashi, T.: JCAP 07, 013 (2020). arXiv:2003.12771

    Article  ADS  Google Scholar 

  37. Aoki, K., Gorji, M.A., Mukohyama, S.: Phys. Lett. B 810, 135843 (2020)

    Article  MathSciNet  Google Scholar 

  38. Aoki, K., Gorji, M.A., Mukohyama, S.: JCAP 09, 014 (2020); JCAP 05 (2021) E01 (erratum); arXiv:2005.08428 [gr-qc]

  39. Jafarzade, K., Zangeneh, M.K., Lobo, F.S.N.: JCAP 04, 008 (2021). arXiv:2010.05755 [gr-qc]

    Article  ADS  Google Scholar 

  40. Fernandes, P.G.S.: Phys. Lett. B 805, 135468 (2020). arXiv:2003.05491 [gr-qc]

    Article  MathSciNet  Google Scholar 

  41. Kumar, A., Ghosh, S.G.: Universe 8(4), 244 (2022). arXiv:2004.01131 [gr-qc]

    Article  ADS  Google Scholar 

  42. Kumar, A., Kumar, R.: Universe 8(4), 232 (2022). arXiv:2003.13104 [gr-qc]

    Article  ADS  Google Scholar 

  43. Yanga, K., Gub, B.-M., Wei, S.-W., Liud, Y.-X.: Eur. Phys. J. C 80, 662 (2020). arXiv:2004.14468 [gr-qc]

    Article  ADS  Google Scholar 

  44. Kruglov, S.I.: Ann. Phys. 428, 168449 (2021). arXiv:2104.08099 [gr-qc]

    Article  Google Scholar 

  45. Kruglov, S.I.: Universe 7(7), 249 (2021). arXiv:2108.07695 [physics.gen-ph]

    Article  ADS  Google Scholar 

  46. Hegde, K., Kumara, A.N., Rizwan, C.L., Ali, M.S.: arXiv:2003.08778 [gr-qc]

  47. Hegde, K., Kumara, A.N., Rizwan, C.A., Ali, M.S., Ajith, K.M.: Ann. Phys. 429, 168461 (2021). arXiv:2007.10259 [gr-qc]

    Article  Google Scholar 

  48. Wei, S.W., Liu, Y.X.: Phys. Rev. D 101, 104018 (2020). arXiv:2003.14275 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  49. Hosseini Mansoori, S.A.: Phys. Dark Univ. 31, 100776 (2021). arXiv:2003.13382 [gr-qc]

    Article  Google Scholar 

  50. Panah, B.E., Jafarzade, K., Hendi, S.: Nucl. Phys. B 961, 115269 (2020). arXiv:2004.04058

    Article  Google Scholar 

  51. Zhang, M., Zhang, C.M., Zou, D.C., Yue, R.H.: Chin. Phys. C 45(4), 045105 (2021). arXiv:2009.03096 [hep-th]

    Article  ADS  Google Scholar 

  52. Ma, Y., Zhang, Y., Zhang, L., Pan, Y.: Chin. J. Phys. 77, 1854–1862 (2022)

    Article  Google Scholar 

  53. Zhang, C.-M., Zou, D.-C., Zhang, M.: Phys. Lett. B 811, 135955 (2020). arXiv:2012.06162 [gr-qc]

    Article  MathSciNet  Google Scholar 

  54. Ghosh, S.G., Singh, D.V., Kumar, R., Maharaj, S.D.: Ann. Phys. 424, 168347 (2021). arXiv:2006.00594 [gr-qc]

    Article  Google Scholar 

  55. Singh, D.V., Bhardwaj, V.K., Upadhyay, S.: Eur. Phys. J. Plus 137(8), 969 (2022). arXiv:2208.13565 [gr-qc]

    Article  Google Scholar 

  56. Singh, D.V., Siwach, S.: Phys. Lett. B 808, 135658 (2020). arXiv:2003.11754 [gr-qc]

    Article  MathSciNet  Google Scholar 

  57. Zhang, M., Zhang, C.M., Zou, D.C., Yue, R.H.: Nucl. Phys. B 973, 115608 (2021). arXiv:2102.04308 [hep-th]

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  59. Ayón-Beato, E., Garcia, A.: Phys. Lett. B 464, 25 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  60. Garcia, A.: Gen. Relativ. Gravit. 31, 629 (1999)

    Article  ADS  Google Scholar 

  61. Cataldo, M., Garcia, A.: Phys. Rev. D 61, 084003 (2000)

    Article  ADS  Google Scholar 

  62. Yang, K., Gu, B.M., Wei, S.W., Liu, Y.X.: Eur. Phys. J. C 80, 662 (2020). arXiv:2004.14468 [gr-qc]

    Article  ADS  Google Scholar 

  63. Kruglov, S.I.: EPL 133, 6 (2021). arXiv:2106.00586 [physics.gen-ph]

    Article  Google Scholar 

  64. Kruglov, S.I.: Symmetry 13, 944 (2021)

    Article  ADS  Google Scholar 

  65. Kruglov, S.I.: Ann. Phys. 428, 168449 (2021). arXiv:2104.08099 [gr-qc]

    Article  Google Scholar 

  66. Jusufi, K.: Ann. Phys. 421, 168285 (2020). arXiv:2005.00360 [gr-qc]

    Article  Google Scholar 

  67. Ghosh, S.G., Singh, D.V., Kumar, R., Maharaj, S.D.: Ann. Phys. 424, 168347 (2021). arXiv:2006.00594 [gr-qc]

    Article  Google Scholar 

  68. Kumar, A., Baboolal, D., Ghosh, S.G.: Universe 8, 244 (2022). arXiv:2004.01131 [gr-qc]

    Article  ADS  Google Scholar 

  69. Mazharimousavi, S.H., Halilsoy, M.: Phys. Rev. D 76, 087501 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  70. Mazharimousavi, S.H., Halilsoy, M., Amirabi, Z.: Phys. Rev. D 78, 064050 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  71. Mazharimousavi, S.H., Halilsoy, M.: Phys. Lett. B 659, 471 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  72. Mazharimousavi, S.H., Halilsoy, M.: Phys. Lett. B 665, 125 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  73. Habib Mazharimousavi, S., Halilsoy, M.: Phys. Lett. B 681, 190–199 (2009). arXiv:0908.0308 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  74. Wu, T.T., Yang, C.N.: In: Mark, H., Fernbach, S. (eds.) Properties of Matter Under Unusual Conditions, p. 389. Interscience, New York (1969)

  75. Yasskin, P.B.: Phys. Rev. D 12, 2212 (1975)

    Article  ADS  MathSciNet  Google Scholar 

  76. Singh, D.V., Singh, B.K., Upadhyay, S.: Ann. Phys. 434, 168642 (2021). arXiv:2203.03861 [gr-qc]

    Article  Google Scholar 

  77. Yerra, P.K., Bhamidipati, C.: Mod. Phys. Lett. A 34, 27 (2019). arXiv:1806.08226

    Article  Google Scholar 

  78. Du, Y.-Z., Li, H.-F., Liu, F., Zhao, R., Zhang, L.-C.: Chin. Phys. C 45, 112001 (2021). arXiv:2112.10403 [hep-th]

    Article  ADS  Google Scholar 

  79. Biswas, A.: Phys. Scr. 96, 125310 (2021). arXiv:2106.11066 [gr-qc]

    Article  ADS  Google Scholar 

  80. Cai, R.-G., Soh, K.-S.: Phys. Rev. D 59, 044013 (1999). arXiv:gr-qc/9808067

    Article  ADS  MathSciNet  Google Scholar 

  81. Cai, R.-G.: Phys. Rev. D 65, 084014 (2002). arXiv:hep-th/0109133

    Article  ADS  MathSciNet  Google Scholar 

  82. Wei, S.-W., Liu, Y.-X.: Phys. Rev. D 101, 104018 (2020). arXiv:2003.14275v3 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  83. Zhang, M., Yang, Z.-Y., Zou, D.-C., Xu, W., Yue, R.-H.: Gen. Relativ. Gravit. 47, 14 (2015). arXiv:1412.1197 [hep-th]

    Article  ADS  Google Scholar 

  84. Hendi, S.H., Eslam Panah, B., Panahiyan, S.: Fortsch. Phys. 66, 1800005 (2018). arXiv:1708.02239 [hep-th]

    Article  ADS  Google Scholar 

  85. Spallucci, E., Smailagic, A.: Phys. Lett. B 723, 436 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  86. Wei, S.W., Liu, Y.X.: Phys. Rev. D 91, 044018 (2015). arXiv:1411.5749 [hep-th]

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We are also grateful to the anonymous referee(s) for valuable comments and suggestions to improve this paper.

Author information

Authors and Affiliations

  1. Department of Physics, Ranaghat College, Ranaghat, 741201, India

    Anindya Biswas

Authors
  1. Anindya Biswas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anindya Biswas.

Ethics declarations

Conflict of interest

The author did not receive support from any organization for the submitted work and has no relevant financial or non-financial interests to disclose.

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

Biswas, A. Black holes in 4D AdS Einstein Gauss Bonnet gravity with power: Yang Mills field. Gen Relativ Gravit 54, 161 (2022). https://doi.org/10.1007/s10714-022-03047-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-022-03047-7

Keywords

Search

Navigation