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The last lost charge and phase transition in Schwarzschild AdS minimally coupled to a cloud of strings

  • Hossein GhaffarnejadEmail author
  • Mohammad Farsam
Regular Article
  • 3 Downloads

Abstract.

In this paper we study the Schwarzschild AdS black hole with a cloud of string background in an extended phase space and investigate a new phase transition related to the topological charge. By treating the topological charge as a new charge for the black hole solution we study its thermodynamics in this new extended phase space. We treat by two approaches to study the phase transition behavior via both T-S and P-v criticality and we find the results confirm each other in a nice way. It is shown that a cloud of strings affects the critical physical quantities and it could be observed an interesting Van der Waals-like phase transition in the extended thermodynamics. The swallow tail-like behavior is also observed in the free energy-temperature diagram. We observe in the \(a\rightarrow 0\) limit that the small/large black hole phase transition reduces to the Hawking-Page phase transition as we expected. We can deduce that the impact of the cloud of strings in the Schwarzschild black hole can bring a Van der Waals-like black hole phase transition.

References

  1. 1.
    S.W. Hawking, D.N. Page, Commun. Math. Phys. 87, 577 (1983)ADSCrossRefGoogle Scholar
  2. 2.
    E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998)MathSciNetCrossRefGoogle Scholar
  4. 4.
    A. Chamblin, R. Emparan, C.V. Johnson, R.C. Myers, Phys. Rev. D 60, 064018 (1999)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    A. Chamblin, R. Emparan, C.V. Johnson, R.C. Myers, Phys. Rev. D 60, 104026 (1999)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    D. Kastor, S. Ray, J. Traschen, Class. Quantum Grav. 26, 195011 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    B.P. Dolan, Class. Quantum Grav. 28, 125020 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    D. Kubiznak, R.B. Mann, JHEP 07, 033 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    S. Dutta, A. Jain, R. Soni, JHEP 13, 60 (2013) hep-th/1310.1748CrossRefGoogle Scholar
  10. 10.
    X.X. Zeng, L.F. Li, hep-th/1512.08855Google Scholar
  11. 11.
    J. Mo, G. Li, X. Xu, Phys. Rev. D 93, 084041 (2016)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    M. Zhang, W. Liul, gr-qc/1610.03648Google Scholar
  13. 13.
    R. Cai, L. Cao, R. Yang, JHEP 09, 005 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    R. Cai, Y. Hu, Q. Pan, Y. Zhang, Phys. Rev. D 91, 024032 (2015)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    J. Mo, G. Li, X. Xu, Eur. Phys. J. C 76, 545 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    R.A. Hennigar, R.B. Mann, Entropy 17, 8056 (2015)ADSCrossRefGoogle Scholar
  17. 17.
    D.C. Zou, S.J. Zhang, B. Wang, Phys. Rev. D 89, 044002 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    N. Altamirano, D. Kubizňák, R. Mann, Z. Sherkatghanad, Class. Quantum Grav. 31, 042001 (2013) hep-th/1308.2672ADSCrossRefGoogle Scholar
  19. 19.
    J.X. Mo, X.X. Zeng, G.Q. Li, X. Jiang, W.B. Liu, JHEP 10, 056 (2013)ADSCrossRefGoogle Scholar
  20. 20.
    J.X. Mo, W.B. Liu, Phys. Lett. B 727, 336 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    N. Altamirano, D. Kubizňák, R. Mann, Phys. Rev. D 88, 101502 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    R. Zhao, H.H. Zhao, M.S. Ma, L.C. Zhang, Eur. Phys. J. C 73, 2645 (2013)ADSCrossRefGoogle Scholar
  23. 23.
    X.-X. Zeng, X.-M. Liu, L.-F. Li, Eur. Phys. J. C 76, 616 (2016)ADSCrossRefGoogle Scholar
  24. 24.
    H. Liu, X.-h. Meng, Mod. Phys. Lett. A 31, 1650199 (2016)ADSCrossRefGoogle Scholar
  25. 25.
    D. Hansen, D. Kubiznak, R.B. Mann, JHEP 01, 047 (2017) gr-qc/1603.05689ADSCrossRefGoogle Scholar
  26. 26.
    A. Rajagopal, D. Kubiznak, R.B. Mann, Phys. Lett. B 737, 277 (2014)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Y. Tian, X.N. Wu, H. Zhang, JHEP 10, 170 (2014)ADSCrossRefGoogle Scholar
  28. 28.
    Y. Tian, gr-qc/1804.00249Google Scholar
  29. 29.
    Shan-Quan Lan, Gu-Qiang Li, Jie-Xiong Mo, Xiao-Bao Xu, gr-qc/1804.06652 (2018)Google Scholar
  30. 30.
    H. Ghaffarnejad, E. Yaraie, M. Farsam, Int. J. Theor. Phys. 57, 1671 (2018)CrossRefGoogle Scholar
  31. 31.
    J.P. Morais Graca, Iarley P. Lobo, I.G. Salako, Chin. Phys. C 42, 063105 (2018) gr-qc/1708.08398ADSCrossRefGoogle Scholar
  32. 32.
    Patricio S. Letelier, Phys. Rev. D 20, 1294 (1979)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    Sushant G. Ghosh, Sunil D. Maharaj, Phys. Rev. D 89, 084027 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    Sushant G. Ghosh, Uma Papnoi, Sunil D. Maharaj, Phys. Rev. D 90, 044068 (2014)ADSCrossRefGoogle Scholar
  35. 35.
    S. Habib Mazharimousavi, M. Halilsoy, Eur. Phys. J. C 76, 95 (2016)ADSCrossRefGoogle Scholar
  36. 36.
    Jefferson de M. Toledo, V.B. Bezerra, Eur. Phys. J. C 78, 534 (2018)ADSCrossRefGoogle Scholar
  37. 37.
    Apratim Ganguly, Sushant G. Ghosh, Sunil D. Maharaj, Phys. Rev. D 90, 064037 (2014)ADSCrossRefGoogle Scholar
  38. 38.
    T.K. Dey, hep-th/1711.07008 (2018)Google Scholar
  39. 39.
    Nigel Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (CRC Press, 2018)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of PhysicsSemnan UniversitySemnanIran

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