Advertisement

Maxwell's equal-area law with several pairs of conjugate variables for RN-AdS black holes

  • Xiong-Ying Guo
  • Huai-Fan LiEmail author
  • Ren Zhao
Regular Article
  • 15 Downloads

Abstract.

In this paper, using Maxwell's equal-area law we study the phase transition of charged AdS black holes by choosing different independent conjugate variables. As is well known, the phase transition can be characterized by the state function of the system, the determination of the phase transition point has nothing to do with the choice of independent conjugate variables. To study the thermodynamic properties of AdS black holes we give the conditions under which the independent conjugate variables are chosen. When the charge of the black hole is invariable, according to the conditions we find that the phase transition is related to the electric potential and the horizon radius of the charged black hole. Keeping the cosmological constant as a fixed parameter, the phase transition of the charged AdS black hole is related to the ratio of the event horizon to the cosmological constant of black holes.

References

  1. 1.
    D. Kubiznak, R.B. Mann, JHEP 07, 033 (2012) arXiv:1205.0559ADSCrossRefGoogle Scholar
  2. 2.
    B.P. Dolan, D. Kastor, D. Kubiznak, R.B. Mann, J. Traschen, Phys. Rev. D 87, 104017 (2013) arXiv:1301.5926ADSCrossRefGoogle Scholar
  3. 3.
    S. Gunasekaran, D. Kubiznak, R.B. Mann, JHEP 11, 110 (2012) arXiv:1208.6251ADSCrossRefGoogle Scholar
  4. 4.
    Rong-Gen Cai, Li-Min Cao, Li Li, Run-Qiu Yang, JHEP 09, 005 (2013) arXiv:1306.6233Google Scholar
  5. 5.
    Y. Sekiwa, Phys. Rev. D 73, 084009 (2006) hep-th/0602269ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Zi-xu Zhao, Ji-liang Jing, JHEP 11, 037 (2014) arXiv:1405.2640ADSCrossRefGoogle Scholar
  7. 7.
    Meng-Sen Ma, Ren Zhao, Yan-Song Liu, Class. Quantum Grav. 34, 165009 (2017) arXiv:1604.06998ADSCrossRefGoogle Scholar
  8. 8.
    Meng-Sen Ma, Rui-Hong Wang, Phys. Rev. D 96, 024052 (2017) arXiv:1707.09156ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    S.H. Hendi, B. Eslam Panah, S. Panahiyan, M.S. Talezadeh, Eur. Phys. J. C 77, 133 (2017) arXiv:1612.00721ADSCrossRefGoogle Scholar
  10. 10.
    Z. Dayyani, A. Sheykhi, M.H. Dehghani, Phys. Rev. D 95, 84004 (2017)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    De-Cheng Zou, Yun-qi Liu, Rui-hong Yue, Eur. Phys. J. C 77, 365 (2017) arXiv:1702.08118ADSCrossRefGoogle Scholar
  12. 12.
    Peng Cheng, Shao-Wen Wei, Yu-Xiao Liu, Phys. Rev. D 94, 024025 (2016) arXiv:1603.08694ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    R. Banerjee, B.R. Majhi, S. Samanta, Phys. Lett. B 767, 25 (2017) arXiv:1611.06701ADSCrossRefGoogle Scholar
  14. 14.
    R. Banerjee, D. Roychowdhury, JHEP 11, 004 (2011) arXiv:1109.2433ADSCrossRefGoogle Scholar
  15. 15.
    R. Banerjee, D. Roychowdhury, Phys. Rev. D 85, 104043 (2012) arXiv:1203.0118ADSCrossRefGoogle Scholar
  16. 16.
    A. Dey, S. Mahapatra, T. Sarkar, Phys. Rev. D 94, 026006 (2016) arXiv:1512.07117ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    K. Bhattacharya, B.R. Majhi, S. Samanta, Phys. Rev. D 96, 084037 (2017)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Xiao-Xiong Zeng, Li-Fang Li, Phys. Lett. B 764, 100 (2017)ADSCrossRefGoogle Scholar
  19. 19.
    A. Dehyadegari, A. Sheykhi, A. Montakhap, Phys. Lett. B 768, 235 (2017) arXiv:1607.05333ADSCrossRefGoogle Scholar
  20. 20.
    Rong-Gen Cai, Shan-Ming Ruan, Shao-Jiang Wang, Run-Qiu Yang, Rong-Hui Peng, JHEP 09, 161 (2016) arXiv:1606.08307ADSGoogle Scholar
  21. 21.
    Jia-Lin Zhang, Rong-Gen Cai, Hongwei Yu, Phys. Rev. D 91, 044028 (2015) arXiv:1502.01428ADSCrossRefGoogle Scholar
  22. 22.
    Jia-Lin Zhang, Rong-Gen Cai, Hongwei Yu, JHEP 02, 143 (2015) arXiv:1409.5305ADSCrossRefGoogle Scholar
  23. 23.
    Shao-Wen Wei, Yu-Xiao Liu, Phys. Rev. D 97, 104027 (2018) arXiv:1711.01522ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Shou-Long Li, Hao. Wei, Phys. Rev. D 99, 064002 (2019) arXiv:1809.03810ADSCrossRefGoogle Scholar
  25. 25.
    Shou-Long, Hong-Da Lyu, Hua-Kai Deng, Hao Wei, Eur. Phys. J. C 79, 201 (2019) arXiv:1809.03471ADSCrossRefGoogle Scholar
  26. 26.
    Yan-Gang Miao, Zhen-Ming Xu, Eur. Phys. J. C 76, 217 (2016) arXiv:1511.00853ADSCrossRefGoogle Scholar
  27. 27.
    Yan-Gang Miao, Zhen-Ming Xu, Eur. Phys. J. C 77, 403 (2017) arXiv:1610.01769ADSCrossRefGoogle Scholar
  28. 28.
    Yi-Fei Wang, Ming Zhang, Wen-Biao Liu, Coexistence curve and molecule number density of AdS topological charged black hole in massive gravity, arXiv:1711.04403Google Scholar
  29. 29.
    A. Dehyadegari, A. Sheykhi, Phys. Rev. D 98, 024011 (2018) arXiv:1711.01151ADSCrossRefGoogle Scholar
  30. 30.
    K. Jafarzade, J. Sadeghi, Phase Transition of charged Rotational Black Hole and Quintessence, arXiv:1710.08642Google Scholar
  31. 31.
    Ren Zhao, Li-Chun Zhang, Commun. Theor. Phys. 70, 578 (2018) arXiv:1710.07225ADSCrossRefGoogle Scholar
  32. 32.
    A. Övgün, Adv. High Energy Phys. 2018, 8153721 (2018) arXiv:1710.06795Google Scholar
  33. 33.
    Z. Dayyani, A. Sheykhi, M.H. Dehghani, S. Hajkhalili, Eur. Phys. J. C 78, 152 (2018) arXiv:1709.06875ADSCrossRefGoogle Scholar
  34. 34.
    M.K. Zangeneh, A. Dehyadegari, A. Sheykhi, R.B. Mann, Phys. Rev. D 97, 084054 (2018) arXiv:1709.04432ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    Ming Zhang, De-Cheng Zou, Rui-Hong Yue, Adv. High Energy Phys. 2017, 3819246 (2017) arXiv:1707.04101Google Scholar
  36. 36.
    A. Sahay, R. Jha, Phys. Rev. D 96, 126017 (2017) arXiv:1707.03629ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Xiao-Xiong Zeng, Yi-Wen Han, Adv. High Energy Phys. 2017, 2356174 (2017) arXiv:1706.02024Google Scholar
  38. 38.
    Shao-Wen Wei, Bin Liang, Yu-Xiao Liu, Phys. Rev. D 96, 124018 (2017) arXiv:1705.08596ADSCrossRefGoogle Scholar
  39. 39.
    Shao-Wen Wei, Yu-Xiao Liu, Phys. Rev. D 87, 044014 (2013) arXiv:1209.1707ADSCrossRefGoogle Scholar
  40. 40.
    Ren Zhao, Hui-Hua Zhao, Meng-Sen Ma, Li-Chun Zhang, Eur. Phys. J. C 73, 2645 (2013)ADSCrossRefGoogle Scholar
  41. 41.
    Huai-fan Li, Meng-Sen Ma, Li-Chun Zhang, Ren Zhao, Nucl. Phys. B 920, 211 (2017)ADSCrossRefGoogle Scholar
  42. 42.
    Huai-fan Li, Hui-Hua Zhao, Li-Chun Zhang, Ren Zhao, Eur. Phys. J. C 77, 295 (2017)ADSCrossRefGoogle Scholar
  43. 43.
    Huai-Fan Li, Xiong-ying Guo, Hui-Hua Zhao, Ren Zhao, Gen. Relativ. Gravit. 49, 111 (2017) arXiv:1610.05428ADSCrossRefGoogle Scholar
  44. 44.
    Hui-Hua Zhao, Li-Chun Zhang, Ren Zhao, Adv. High Energy Phys. 2016, 2021748 (2016)Google Scholar
  45. 45.
    Hui-Hua Zhao, Li-Chun Zhang, Meng-Sen Ma, Ren Zhao, Class. Quantum Grav. 32, 145007 (2015)ADSCrossRefGoogle Scholar
  46. 46.
    Li-Chun Zhang, Hui-Hua Zhao, Ren Zhao, Meng-Sen Ma, Adv. High Energy Phys. 2014, 816728 (2014)Google Scholar
  47. 47.
    A. Belhaj, M. Chabab, H. Ei Moumni, K. Masmar, M.B. Sedra, Eur. Phys. J. C 75, 71 (2015)ADSCrossRefGoogle Scholar
  48. 48.
    E. Spallucci, A. Smailagic, Phys. Lett. B 723, 436 (2013) arXiv:1305.3379ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    D. Kastor, S. Ray, J. Traschen, Class. Quantum. Grav. 26, 195011 (2009)ADSCrossRefGoogle Scholar
  50. 50.
    J.D. Bekenstein, Lett. Nuovo Cimento 4, 737 (1972)ADSCrossRefGoogle Scholar
  51. 51.
    J.D. Bekenstein, Phys. Rev. D 9, 3292 (1974)ADSCrossRefGoogle Scholar
  52. 52.
    J.D. Bekenstein, Phys. Rev. D 7, 949 (1973)ADSCrossRefGoogle Scholar
  53. 53.
    J.M. Bardeen, B. Carter, S.W. Hawking, Commun. Math. Phys. 31, 161 (1973)ADSCrossRefGoogle Scholar
  54. 54.
    S.W. Hawking, Nature 248, 30 (1974)ADSCrossRefGoogle Scholar
  55. 55.
    S.W. Hawking, Commun. Math. Phys. 43, 199 (1975)ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of PhysicsShanxi Datong UniversityDatongChina
  2. 2.Institute of Theoretical PhysicsShanxi Datong UniversityDatongChina

Personalised recommendations