Phases of global AdS black holes

  • Pallab Basu
  • Chethan Krishnan
  • P.N. Bala Subramanian
Open Access
Regular Article - Theoretical Physics


We study the phases of gravity coupled to a charged scalar and gauge field in an asymptotically Anti-de Sitter spacetime (AdS 4) in the grand canonical ensemble. For the conformally coupled scalar, an intricate phase diagram is charted out between the four relevant solutions: global AdS, boson star, Reissner-Nordstrom black hole and the hairy black hole. The nature of the phase diagram undergoes qualitative changes as the charge of the scalar is changed, which we discuss. We also discuss the new features that arise in the extremal limit.


AdS-CFT Correspondence Black Holes 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].ADSGoogle Scholar
  6. [6]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    P. Basu, J. Bhattacharya, S. Bhattacharyya, R. Loganayagam, S. Minwalla and V. Umesh, Small Hairy Black Holes in Global AdS Spacetime, JHEP 10 (2010) 045 [arXiv:1003.3232] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    O.J.C. Dias, P. Figueras, S. Minwalla, P. Mitra, R. Monteiro and J.E. Santos, Hairy black holes and solitons in global AdS 5, JHEP 08 (2012) 117 [arXiv:1112.4447] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    J. Markeviciute and J.E. Santos, Hairy Black Holes in AdS 5 × S 5, arXiv:1602.03893 [INSPIRE].
  11. [11]
    S. Bhattacharyya, S. Minwalla and K. Papadodimas, Small Hairy Black Holes in AdS 5 × S 5, JHEP 11 (2011) 035 [arXiv:1005.1287] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    S.W. Hawking and H.S. Reall, Charged and rotating AdS black holes and their CFT duals, Phys. Rev. D 61 (2000) 024014 [hep-th/9908109] [INSPIRE].ADSMathSciNetGoogle Scholar
  13. [13]
    A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS Black Holes and Catastrophic Holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].ADSMathSciNetGoogle Scholar
  14. [14]
    Y. Brihaye, B. Hartmann and S. Tojiev, Stability of charged solitons and formation of boson stars in 5-dimensional Anti-de Sitter space-time, Class. Quant. Grav. 30 (2013) 115009 [arXiv:1301.2452] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  15. [15]
    S.A. Gentle, M. Rangamani and B. Withers, A Soliton Menagerie in AdS, JHEP 05 (2012) 106 [arXiv:1112.3979] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    G.T. Horowitz and B. Way, Complete Phase Diagrams for a Holographic Superconductor/Insulator System, JHEP 11 (2010) 011 [arXiv:1007.3714] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  17. [17]
    T. Nishioka, S. Ryu and T. Takayanagi, Holographic Superconductor/Insulator Transition at Zero Temperature, JHEP 03 (2010) 131 [arXiv:0911.0962] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  18. [18]
    P. Basu, F. Nogueira, M. Rozali, J.B. Stang and M. Van Raamsdonk, Towards A Holographic Model of Color Superconductivity, New J. Phys. 13 (2011) 055001 [arXiv:1101.4042] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    P. Basu and S.R. Das, Quantum Quench across a Holographic Critical Point, JHEP 01 (2012) 103 [arXiv:1109.3909] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  20. [20]
    P. Bizon and A. Rostworowski, On weakly turbulent instability of anti-de Sitter space, Phys. Rev. Lett. 107 (2011) 031102 [arXiv:1104.3702] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    V. Balasubramanian, A. Buchel, S.R. Green, L. Lehner and S.L. Liebling, Holographic Thermalization, Stability of Anti-de Sitter Space and the Fermi-Pasta-Ulam Paradox, Phys. Rev. Lett. 113 (2014) 071601 [arXiv:1403.6471] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    B. Craps, O. Evnin and J. Vanhoof, Renormalization group, secular term resummation and AdS (in)stability, JHEP 10 (2014) 048 [arXiv:1407.6273] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    P. Basu, C. Krishnan and A. Saurabh, A stochasticity threshold in holography and the instability of AdS, Int. J. Mod. Phys. A 30 (2015) 1550128 [arXiv:1408.0624] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    B. Craps, O. Evnin and J. Vanhoof, Renormalization, averaging, conservation laws and AdS (in)stability, JHEP 01 (2015) 108 [arXiv:1412.3249] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  25. [25]
    P. Basu, C. Krishnan and P.N. Bala Subramanian, AdS (In)stability: Lessons From The Scalar Field, Phys. Lett. B 746 (2015) 261 [arXiv:1501.07499] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    O. Evnin and C. Krishnan, A Hidden Symmetry of AdS Resonances, Phys. Rev. D 91 (2015) 126010 [arXiv:1502.03749] [INSPIRE].ADSMathSciNetGoogle Scholar
  27. [27]
    P. Basu, A. Mukherjee and H.-H. Shieh, Supercurrent: Vector Hair for an AdS Black Hole, Phys. Rev. D 79 (2009) 045010 [arXiv:0809.4494] [INSPIRE].ADSGoogle Scholar
  28. [28]
    C.P. Herzog, P.K. Kovtun and D.T. Son, Holographic model of superfluidity, Phys. Rev. D 79 (2009) 066002 [arXiv:0809.4870] [INSPIRE].ADSMathSciNetGoogle Scholar
  29. [29]
    D. Arean, P. Basu and C. Krishnan, The Many Phases of Holographic Superfluids, JHEP 10 (2010) 006 [arXiv:1006.5165] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  30. [30]
    D. Arean, M. Bertolini, C. Krishnan and T. Prochazka, Type IIB Holographic Superfluid Flows, JHEP 03 (2011) 008 [arXiv:1010.5777] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Pallab Basu
    • 1
  • Chethan Krishnan
    • 2
  • P.N. Bala Subramanian
    • 2
  1. 1.International Center for Theoretical SciencesBangaloreIndia
  2. 2.Center for High Energy PhysicsIndian Institute of ScienceBangaloreIndia

Personalised recommendations