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Exploring the phase transition in charged Gauss–Bonnet black holes: a holographic thermodynamics perspectives

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Abstract

In this paper, we delve into the study of thermodynamics and phase transition of charged Gauss–Bonnet black holes within the context of anti-de Sitter space, with particular emphasis on the central charge’s role within the dual conformal field theory (CFT). We employ a holographic methodology that interprets the cosmological constant and the Newton constant as thermodynamic variables, leading to the derivation of a modified first law of thermodynamics that incorporates the thermodynamic volume and pressure. Our findings reveal that the central charge of the CFT is intrinsically linked to the variation of these constants, and its stability can be ensured by simultaneous adjustment of these constants. We further explore the phase structures of the black holes, utilizing the free energy. Our research uncovers the existence of a critical value of the central charge, beyond which the phase diagram displays a first-order phase transition between small and large black holes. We also delve into the implications of our findings on the complexity of the CFT. Our conclusions underscore the significant role of the central charge in the holographic thermodynamics and phase transition of charged Gauss–Bonnet black holes. Furthermore, we conclude that while the central charge considered provides suitable and satisfactory solutions for this black hole in 4 and 5 dimensions, it becomes necessary to introduce a unique central charge for this structure of modified gravity. In essence, the central charge in holographic thermodynamics is not a universal value and requires modification in accordance with different modified gravities. Consequently, the physics of the problem will significantly deviate from the one discussed in this article, indicating a rich and complex landscape for future work.

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References

  1. Bardeen, J.M., Carter, B., Hawking, S.W.: The four laws of black hole mechanics. Commun. Math. Phys. 31, 161–170 (1973)

    ADS  MathSciNet  Google Scholar 

  2. Davies, P.C.W.: Thermodynamics of black holes. Rep. Prog. Phys. 41(8), 1313 (1978)

    ADS  Google Scholar 

  3. Hawking, S.W., Page, D.N.: Thermodynamics of black holes in anti-de Sitter space. Commun. Math. Phys. 87, 577–588 (1983)

    ADS  MathSciNet  Google Scholar 

  4. Wald, R.M.: The thermodynamics of black holes. Living Rev. Relat. 4, 1–44 (2001)

    ADS  Google Scholar 

  5. Hawking, S.W.: Black holes and thermodynamics. Phys. Rev. D 13(2), 191 (1976)

    ADS  Google Scholar 

  6. Bekenstein, J.D.: Black-hole thermodynamics. Phys. Today 33(1), 24–31 (1980)

    ADS  MathSciNet  Google Scholar 

  7. Wald, R.M.: Black Holes and Thermodynamics. Black Holes and Relativistic Stars, pp. 155–176 (1998)

  8. Hayward, S.A.: Unified first law of black-hole dynamics and relativistic thermodynamics. Class. Quantum Gravity 15(10), 3147 (1998)

    ADS  MathSciNet  Google Scholar 

  9. Carter, B.M.N., Neupane, I.P.: Thermodynamics and stability of higher dimensional rotating (Kerr-) AdS black holes. Phys. Rev. D 72(4), 043534 (2005)

    ADS  MathSciNet  Google Scholar 

  10. Ruppeiner, G.: Thermodynamic black holes. Entropy 20(6), 460 (2018)

    ADS  MathSciNet  Google Scholar 

  11. Xiao, Y., Tian, Yu., Liu, Y.-X.: Extended black hole thermodynamics from extended Iyer–Wald formalism. Phys. Rev. Lett. 132(2), 021401 (2024)

    ADS  MathSciNet  Google Scholar 

  12. Minamitsuji, M., Kei-ichi, M.: Black hole thermodynamics in generalized Proca theories. (2024) arXiv preprint arXiv:2403.08986

  13. Bardeen, J.M.: Kerr metric black holes. Nature 226(5240), 64–65 (1970)

    ADS  Google Scholar 

  14. Bardeen, J.M.: Properties of black holes relevant to their observation. In: Symposium-International Astronomical Union, vol. 64. Cambridge University Press, Cambridge (1974)

  15. Bardeen, J.M.: Timelike and null geodesics in the Kerr metric. Black Holes 215, 66 (1973)

    Google Scholar 

  16. Kastor, D., Ray, S., Traschen, J.: Enthalpy and the mechanics of AdS black holes. Class. Quantum Gravity 26(19), 195011 (2009)

    ADS  MathSciNet  Google Scholar 

  17. Kubiznak, D., Mann, R.B.: P–V criticality of charged AdS black holes. J. High Energy Phys. 2012(7), 1–25 (2012)

    MathSciNet  Google Scholar 

  18. Cai, R.-G.: Gauss–Bonnet black holes in AdS spaces. Phys. Rev. D 65(8), 084014 (2002)

    ADS  MathSciNet  Google Scholar 

  19. Altamirano, N., et al.: Kerr-AdS analogue of triple point and solid/liquid/gas phase transition. Class. Quantum Gravity 31(4), 042001 (2014)

    ADS  MathSciNet  Google Scholar 

  20. Altamirano, N., Kubizňák, D., Mann, R.B.: Reentrant phase transitions in rotating anti-de Sitter black holes. Phys. Rev. D 88(10), 101502 (2013)

    ADS  Google Scholar 

  21. Dutta, S., Jain, A., Soni, R.: Dyonic black hole and holography. J. High Energy Phys. 2013(12), 1–30 (2013)

    Google Scholar 

  22. Johnson, C.V.: Holographic heat engines. Class. Quantum Gravity 31(20), 205002 (2014)

    ADS  Google Scholar 

  23. Kubizňák, D., Mann, R.B.: Black hole chemistry. Can. J. Phys. 93(9), 999–1002 (2015)

    ADS  Google Scholar 

  24. Kubizňák, D., Mann, R.B., Teo, M.: Black hole chemistry: thermodynamics with Lambda. Class. Quantum Gravity 34(6), 063001 (2017)

    ADS  MathSciNet  Google Scholar 

  25. Banerjee, R., Roychowdhury, D.: Thermodynamics of phase transition in higher dimensional AdS black holes. J. High Energy Phys. 2011(11), 1–13 (2011)

    Google Scholar 

  26. Mandal, A., Samanta, S., Majhi, B.R.: Phase transition and critical phenomena of black holes: a general approach. Phys. Rev. D 94(6), 064069 (2016)

    ADS  MathSciNet  Google Scholar 

  27. Maity, R., Roy, P., Sarkar, T.: Black hole phase transitions and the chemical potential. Phys. Lett. B 765, 386–394 (2017)

    ADS  Google Scholar 

  28. Silva, P.J.: Phase transitions and statistical mechanics for BPS black holes in AdS/CFT. J. High Energy Phys. 3, 15 (2007)

    ADS  MathSciNet  Google Scholar 

  29. El Moumni, H.: Revisiting the phase transition of AdS–Maxwell–Power–Yang–Mills black holes via AdS/CFT tools. Phys. Lett. B 776, 124–132 (2018)

    ADS  MathSciNet  Google Scholar 

  30. Sokolowski, L.M., Mazur, P.: Second-order phase transitions in black-hole thermodynamics. J. Phys. A Math. Gen. 13(3), 1113 (1980)

    ADS  MathSciNet  Google Scholar 

  31. Wei, S.-W., Liu, Y.-X.: Insight into the microscopic structure of an AdS black hole from a thermodynamical phase transition. Phys. Rev. Lett. 115(11), 111302 (2015)

    ADS  Google Scholar 

  32. Li, R., Wang, J.: Thermodynamics and kinetics of Hawking–Page phase transition. Phys. Rev. D 102(2), 024085 (2020)

    ADS  MathSciNet  Google Scholar 

  33. Aharony, O., Urbach, E.Y., Weiss, M.: Generalized Hawking–Page transitions. J. High Energy Phys. 2019(8), 1–21 (2019)

    MathSciNet  Google Scholar 

  34. Wei, S.-W., Liu, Y.-X., Mann, R.B.: Novel dual relation and constant in Hawking–Page phase transitions. Phys. Rev. D 102(10), 104011 (2020)

    ADS  MathSciNet  Google Scholar 

  35. Belhaj, A., et al.: On universal constants of AdS black holes from Hawking–Page phase transition. Phys. Lett. B 811, 135871 (2020)

    MathSciNet  Google Scholar 

  36. Barzi, F., El Moumni, H., Masmar, K.: Rényi topology of charged-flat black hole: Hawking–Page and Van-der-Waals phase transitions. J. High Energy Astrophys. 6, 66 (2024)

    Google Scholar 

  37. Wei, S.-W., Liu, Y.-X.: Topology of black hole thermodynamics. Phys. Rev. D 105(10), 104003 (2022)

    ADS  MathSciNet  Google Scholar 

  38. Yerra, P.K., Bhamidipati, C.: Topology of black hole thermodynamics in Gauss–Bonnet gravity. Phys. Rev. D 105(10), 104053 (2022)

    ADS  MathSciNet  Google Scholar 

  39. Bai, N.-C., Li, L., Tao, J.: Topology of black hole thermodynamics in Lovelock gravity. Phys. Rev. D 107(6), 064015 (2023)

    ADS  MathSciNet  Google Scholar 

  40. Wei, S.-W., Liu, Y.-X., Mann, R.B.: Black hole solutions as topological thermodynamic defects. Phys. Rev. Lett. 129(19), 191101 (2022)

    ADS  MathSciNet  Google Scholar 

  41. Wu, D.: Topological classes of rotating black holes. Phys. Rev. D 107(2), 024024 (2023)

    ADS  MathSciNet  Google Scholar 

  42. Wu, D.: Topological classes of thermodynamics of the four-dimensional static accelerating black holes. Phys. Rev. D 108(8), 084041 (2023)

    ADS  MathSciNet  Google Scholar 

  43. Sadeghi, J., et al.: Thermodynamic topology of black holes from bulk-boundary, extended, and restricted phase space perspectives. Ann. Phys. 66, 169569 (2023)

    MathSciNet  Google Scholar 

  44. Zhang, M.-Y., et al.: Topology of nonlinearly charged black hole chemistry via massive gravity. Eur. Phys. J. C 83, 773 (2023)

    ADS  Google Scholar 

  45. Alipour, M.R., et al.: Topological classification and black hole thermodynamics. Phys. Dark Univ. 42, 101361 (2023)

    Google Scholar 

  46. Sadeghi, J., et al.: Bulk-boundary and RPS thermodynamics from Topology perspective (2023). arXiv preprint arXiv:2306.16117

  47. Sadeghi, J., et al.: Bardeen black hole thermodynamics from topological perspective. Ann. Phys. 66, 169391 (2023)

    MathSciNet  Google Scholar 

  48. Zhang, M., Jiang, J.: Bulk-boundary thermodynamic equivalence: a topology viewpoint. J. High Energy Phys. 2023(6), 1–17 (2023)

    MathSciNet  Google Scholar 

  49. Sadeghi, J., et al.: Topology of Hayward-AdS black hole thermodynamics. Phys. Scr. 99, 025003 (2024)

    ADS  Google Scholar 

  50. Sadeghi, J., et al.: Thermodynamic topology and photon spheres in the hyperscaling violating black holes. Astropart. Phys. 66, 102–920 (2023)

    Google Scholar 

  51. Dutta, S., Punia, G.S.: String theory corrections to holographic black hole chemistry. Phys. Rev. D 106(2), 026003 (2022)

    ADS  MathSciNet  Google Scholar 

  52. Sinamuli, M., Mann, R.B.: Higher order corrections to holographic black hole chemistry. Phys. Rev. D 96(8), 086008 (2017)

    ADS  MathSciNet  Google Scholar 

  53. Mir, M., et al.: Black hole chemistry and holography in generalized quasi-topological gravity. J. High Energy Phys. 2019(8), 1–70 (2019)

    MathSciNet  Google Scholar 

  54. Kubizňák, D., Mann, R.B., Teo, M.: Black hole chemistry: thermodynamics with Lambda. Class. Quantum Gravity 34(6), 063001 (2017)

    ADS  MathSciNet  Google Scholar 

  55. Haro, D., Sebastian, K.S., Solodukhin, S.N.: Holographic reconstruction of spacetime and renormalization in the ads/cft correspondence. Commun. Math. Phys. 217, 595–622 (2001)

    ADS  MathSciNet  Google Scholar 

  56. Rivelles, V.O.: Holographic principle and ads/cft correspondence. arXiv preprint arXiv:hep-th/9912139 (1999)

  57. Dobashi, S., Yoneya, T.: Resolving the holography in the plane-wave limit of AdS/CFT correspondence. Nucl. Phys. B 711(1–2), 3–53 (2005)

    ADS  MathSciNet  Google Scholar 

  58. Damghan, I.: Holography and Its Applications (ICHA2 2023) (2023)

  59. Karch, A., Robinson, B.: Holographic black hole chemistry. J. High Energy Phys. 2015(12), 1–15 (2015)

    MathSciNet  Google Scholar 

  60. Mir, M., et al.: Black hole chemistry and holography in generalized quasi-topological gravity. J. High Energy Phys. 2019(8), 1–70 (2019)

    MathSciNet  Google Scholar 

  61. Karch, A., Robinson, B.: Holographic black hole chemistry. J. High Energy Phys. 2015(12), 1–15 (2015)

    MathSciNet  Google Scholar 

  62. Sinamuli, M., Mann, R.B.: Higher order corrections to holographic black hole chemistry. Phys. Rev. D 96(8), 086008 (2017)

    ADS  MathSciNet  Google Scholar 

  63. Visser, M.R.: Holographic thermodynamics requires a chemical potential for color. Phys. Rev. D 105(10), 106014 (2022)

    ADS  MathSciNet  Google Scholar 

  64. Gibbons, G., Kallosh, R., Kol, B.: Moduli, scalar charges, and the first law of black hole thermodynamics. Phys. Rev. Lett. 77(25), 4992 (1996)

    ADS  Google Scholar 

  65. DE Creighton, J., Mann, R.B.: Quasilocal thermodynamics of dilaton gravity coupled to gauge fields. Phys. Rev. D 52(8), 4569 (1995)

    ADS  MathSciNet  Google Scholar 

  66. Cong, W., Kubizňák, D., Mann, R.B.: Thermodynamics of AdS black holes: critical behavior of the central charge. Phys. Rev. Lett. 127(9), 091301 (2021)

    ADS  MathSciNet  Google Scholar 

  67. Qu, Y., Tao, J., Yang, H.: Thermodynamics and phase transition in central charge criticality of charged Gauss–Bonnet AdS black holes. Nucl. Phys. B 992, 116234 (2023)

    MathSciNet  Google Scholar 

  68. Alfaia, R.B., Lobo, I.P., Brito, L.C.T.: Central charge criticality of charged AdS black hole surrounded by different fluids. Eur. Phys. J. Plus 137(3), 402 (2022)

    Google Scholar 

  69. Gao, Z., Zhao, L.: Restricted phase space thermodynamics for AdS black holes via holography. Class. Quantum Gravity 39(7), 075019 (2022)

    ADS  MathSciNet  Google Scholar 

  70. Gao, Z., Kong, X., Zhao, L.: Thermodynamics of Kerr-AdS black holes in the restricted phase space. Eur. Phys. J. C 82(2), 112 (2022)

    ADS  Google Scholar 

  71. Alipour, M.R., Sadeghi, J., Shokri, M.: WGC and WCCC of black holes with quintessence and cloud strings in RPS space. Nucl. Phys. B 990, 116184 (2023)

    MathSciNet  Google Scholar 

  72. Sadeghi, J., et al.: RPS thermodynamics of Taub-NUT AdS black holes in the presence of central charge and the weak gravity conjecture. Gener. Relat. Gravit. 54(10), 129 (2022)

    ADS  MathSciNet  Google Scholar 

  73. Kumar, N., Sen, S., Gangopadhyay, S.: Phase transition structure and breaking of universal nature of central charge criticality in a Born–Infeld AdS black hole. Phys. Rev. D 106(2), 026005 (2022)

    ADS  MathSciNet  Google Scholar 

  74. Wang, Y., Ren, J.: Thermodynamics of hairy accelerating black holes in gauged supergravity and beyond. Phys. Rev. D 106(10), 104046 (2022)

    ADS  MathSciNet  Google Scholar 

  75. Lobo, I.P., et al.: Holographic dictionary for generic asymptotically AdS black holes (2022). arXiv preprint arXiv:2206.13664

  76. Ghosh, A., Chandrasekhar, B., Sudipta, M.: Logarithmic corrections to black hole entropy and holography (2022). arXiv preprint arXiv:2207.02820

  77. Bai, Y.-Y., et al.: Revisit on thermodynamics of BTZ black hole with variable Newton constant (2022). arXiv preprint arXiv:2208.11859

  78. Dutta, S., Punia, G.S.: String theory corrections to holographic black hole chemistry. Phys. Rev. D 106(2), 026003 (2022)

    ADS  MathSciNet  Google Scholar 

  79. Ahmed, M.B., et al.: Holographic dual of extended black hole thermodynamics. Phys. Rev. Lett. 130(18), 181401 (2023)

    ADS  MathSciNet  Google Scholar 

  80. Johnson, C.V.: Holographic heat engines. Class. Quantum Gravity 31(20), 205002 (2014)

    ADS  Google Scholar 

  81. Dolan, B.P.: Bose condensation and branes. J. High Energy Phys. 2014(10), 1–8 (2014)

    MathSciNet  Google Scholar 

  82. Kastor, D., Ray, S., Traschen, J.: Chemical potential in the first law for holographic entanglement entropy. J. High Energy Phys. 2014(11), 1–17 (2014)

    Google Scholar 

  83. Zhang, J.-L., Cai, R.-G., Hongwei, Yu.: Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in AdS5 \(\times \) S5 spacetime. J. High Energy Phys. 2015(2), 1–16 (2015)

    Google Scholar 

  84. Dolan, B.P.: Pressure and compressibility of conformal field theories from the AdS/CFT correspondence. Entropy 18(5), 169 (2016)

    ADS  Google Scholar 

  85. Maldacena, J.: The large-N limit of superconformal field theories and supergravity. Int. J. Theor. Phys. 38(4), 1113–1133 (1999)

    MathSciNet  Google Scholar 

  86. Visser, M.R.: Holographic thermodynamics requires a chemical potential for color. Phys. Rev. D 105(10), 106014 (2022)

    ADS  MathSciNet  Google Scholar 

  87. Ahmed, M.B., et al.: Holographic dual of extended black hole thermodynamics. Phys. Rev. Lett. 130(18), 181401 (2023)

    ADS  MathSciNet  Google Scholar 

  88. Cong, W., et al.: Holographic CFT phase transitions and criticality for charged AdS black holes. J. High Energy Phys. 2022(8), 1–37 (2022)

    MathSciNet  Google Scholar 

  89. Gong, T.-F., Jiang, J., Zhang, M.: Holographic thermodynamics of rotating black holes. J. High Energy Phys. 2023(6), 1–22 (2023)

    MathSciNet  Google Scholar 

  90. Ahmed, M.B., et al.: Holographic CFT phase transitions and criticality for rotating AdS black holes. J. High Energy Phys. 2023(8), 1–32 (2023)

    MathSciNet  Google Scholar 

  91. Qu, Y., Tao, J., Yang, H.: Thermodynamics and phase transition in central charge criticality of charged Gauss–Bonnet AdS black holes. Nucl. Phys. B 992, 116234 (2023)

    MathSciNet  Google Scholar 

  92. Parikh, M.: Enhanced instability of de Sitter space in Einstein–Gauss–Bonnet gravity. Phys. Rev. D 84(4), 044048 (2011)

    ADS  MathSciNet  Google Scholar 

  93. Chakravarti, K., Ghosh, R., Sarkar, S.: Constraining the topological Gauss–Bonnet coupling from GW150914. Phys. Rev. D 106(4), L041503 (2022)

    ADS  Google Scholar 

  94. Li, H.-L., Zeng, X.-X., Lin, R.: Holographic phase transition from novel Gauss–Bonnet AdS black holes. Eur. Phys. J. C 80(7), 652 (2020)

    ADS  Google Scholar 

  95. Glavan, D., Lin, C.: Einstein–Gauss–Bonnet gravity in four-dimensional spacetime. Phys. Rev. Lett. 124(8), 081301 (2020)

    ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran

    Jafar Sadeghi, Mohammad Reza Alipour, Mohammad Ali S. Afshar & Saeed Noori Gashti

  2. School of Physics, Damghan University, P.O. Box 3671641167, Damghan, Iran

    Saeed Noori Gashti

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  1. Jafar Sadeghi
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  2. Mohammad Reza Alipour
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  3. Mohammad Ali S. Afshar
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  4. Saeed Noori Gashti
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Contributions

J. Sadeghi: Conceptualization, Methodology. M. R Alipour: Visualization, Investigation. M.A.S Afshar: Writing—original draft. S. Noori Gashti:: Writing—review & editing, Visualization.

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Correspondence to Saeed Noori Gashti.

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Sadeghi, J., Alipour, M.R., Afshar, M.A.S. et al. Exploring the phase transition in charged Gauss–Bonnet black holes: a holographic thermodynamics perspectives. Gen Relativ Gravit 56, 93 (2024). https://doi.org/10.1007/s10714-024-03285-x

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